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pooja195
 one year ago
@mathmate
pooja195
 one year ago
@mathmate

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mathmate
 one year ago
Best ResponseYou've already chosen the best response.1Start with quadratic equations, ok?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1Solve \(x^2 6x +9=0\)

pooja195
 one year ago
Best ResponseYou've already chosen the best response.1\[\huge~x=\frac{ (6)\pm \sqrt{(6)^24(1)(9)} }{ 2(1) } \]

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1Great, now can you simplify that, because it will be greatly simplified when you put the numbers in there.

pooja195
 one year ago
Best ResponseYou've already chosen the best response.1\[\huge~x=\frac{ 6\pm \sqrt{0} }{ 2}\]

pooja195
 one year ago
Best ResponseYou've already chosen the best response.1\[\huge~\frac{ 6 }{ 2 }=3~~~~~x=3\]

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1Yes, that is the same as {3,3}, or 3 (twice)

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1It's called a double root, andthe graph looks like this:dw:1433211976391:dw the vertex just touches the xaxis.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1If you factored, you would have got (x3)^2=0, which is the same as saying (x3)=0, or x=3 (twice), or x={3,3}

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1Was wondering you still have the online textbook?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1Can you dig some questions out of there, which will be more like what you have learned.

pooja195
 one year ago
Best ResponseYou've already chosen the best response.1T_T but there are answers ,_,

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1You don't have to look at them, in any case, we are looking at the work, can check the answers at the end.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1There may be word problems, which take more time to make. Using readymade problems can help us do more.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1Have you done anything like this? "A picture has a height that is 4/3 its width. It is to be enlarged to have an area of 192 square inches. What will be the dimensions of the enlargement?"

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1Always the numerical equations, and nothing like word problems?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1ok, so we can skip that.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1Whenever you solve quadratics, there are three ways to do it. If the teacher does not specify, you can use any method you want. If he/she specifies completing the square, you have no choice. the three are:

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1quad formula (just did) factoring (did over the weekend) completing the square Do youknow how to do the last one?

pooja195
 one year ago
Best ResponseYou've already chosen the best response.1no :/ we havent learned it

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1ok, so we skip that too. Anything else you'd like to do on quadratic equations/

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1So we will move onto system of linear equations. Have you done word problems?

pooja195
 one year ago
Best ResponseYou've already chosen the best response.1yes but dont like those :/

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1How many ways do you know to solve system of linear equations?

pooja195
 one year ago
Best ResponseYou've already chosen the best response.1Elmination Substituion :/

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1When you have y=2x+3 y=4x2 then you equate the righthand sides (since they both equal y) to give 4x2=2x+3 and solve for x. It is a form of elimination, but makes life easier. (called method of comparison)

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1Ok, so let go: Solve y = 36 – 9x 3x + y/3 = 12

pooja195
 one year ago
Best ResponseYou've already chosen the best response.13x+(369x)/3=12 6x+36/3=12 6x+12=12 x=0

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1...not finished! need y, and the final answer!

pooja195
 one year ago
Best ResponseYou've already chosen the best response.1y=369(0) y=360 y=36? (0,36)

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1Solve the following system by substitution. 2x – 3y = –2 4x + y = 24 When you see a singleton y, or singleton x, then you can try substitution, as in the above case.

pooja195
 one year ago
Best ResponseYou've already chosen the best response.1y=4x+24 2x3y=2 2x3(4x+24)=2 2x+12x72=2 14x72=2 14x=70 x=5 y=4(5)+24 y=20+24 y=44 Final answer (5,44)

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1Something wrong here, otherwise all correct. y=4(5)+24 y=20+24 y=44

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1yep! Solve the following system using addition (a kind of elimination) 2x + y = 9 3x – y = 16

pooja195
 one year ago
Best ResponseYou've already chosen the best response.1x=5 2(5)+y=9 10+y=9 y=1 (5,1)

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1That was fast! You solved for x by inspection! But show work in exams!

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1The admission fee at a small fair is $1.50 for children and $4.00 for adults. On a certain day, 2200 people enter the fair and $5050 is collected. How many children and how many adults attended?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1With word problems, always define variables first, so you don't get confused at the end.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1I'll do this one, ok?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1Define variables: Number of children = c Number of adults = a (we'll could get confused using x,y, but never this way)

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1Admission for children = $1.50 Admission for adults = $4

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1"2200 people enter the fair and $5050 is collected" means c+a = 2200 1.50c + 4a=5050 = 15c+40a = 50500 (keep integers as long as possible Substitute (because c has a coefficient of 1) c=2200a so 15(2200a) + 40a = 50500 expand 33000 15a + 40a = 50500

mathmate
 one year ago
Best ResponseYou've already chosen the best response.140a15a = 5050033000 25a = 17500 a=17500/25 = 700 c=2200700=1500 Check 1.5c+4a=2250+2800=5050 good!

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1You will find that once the variables are defined, everything else look easy. What do you think?

pooja195
 one year ago
Best ResponseYou've already chosen the best response.1It seems so complicated >_<

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1Do you want to tell me which part is harder to understand?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1It looks complicated probably because I show all the work. If I skipped or jumped some steps, it will look easy, but a little harder to follow.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1Now your turn! The sum of the digits of a twodigit number is 7. When the digits are reversed, the number is increased by 27. Find the number

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1First define variables, use meaningful names, like t = tens digit u = units digit. so far so good?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1When you have a number like 25, then t=2, u=5, and 10t+u = 25.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1"The sum of the digits of a twodigit number is 7" can you form an equation with that?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1Here, we are saying the equivalent of 2+5=7, so t+u=7 will do. now "When the digits are reversed, the number is increased by 27. "

mathmate
 one year ago
Best ResponseYou've already chosen the best response.110t+u is the original number 10u+t is the number reversed (units digit becomes 10's digit) so 10u+t = 10t+u + 27 (increased by 27)

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1Simplifying this equation, we get 9u9t=27 or ut=3 combined with u+t=7 we solve for t=2, u=5, or the original number is 25.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1I'm typing up an example.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1\(\large \frac{5}{x^21}+\frac{4}{x^2+2x+1}\)

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1So first factorize the denominators:

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1\(\frac{5}{(x+1)(x1)}+\frac{4}{(x+1)^2}\)

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1Can you find the common denominator? between (x+1)(x1) and (x+1)^2

pooja195
 one year ago
Best ResponseYou've already chosen the best response.1and then x+1 on the other side?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1"common" denominator of two expressions must contain ALL the factors, and is the same for all the terms. So start with one of the two , say (x+1)(x1) and add factors to it so that it contains every expression.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1Say we start with (x+1)(x1), surely it contains (x+1)(x1) , which is the first expression.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1Question is, does it contain the second expression (x+1)^2?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1the answer is no. What do we need to do? Multiply by another (x+1), so we end up with a common denominator of (x+1)(x1)(x+1).

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1So going back to the question: \(\Large \frac{5\color{red}{(x+1)}}{(x+1)(x1)\color{red}{(x+1)}}+\frac{4\color{blue}{(x1)}}{(x+1)^2\color{blue}{(x1)}}\) notice that now both denominators are identical.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1\(\Large \frac{5\color{red}{(x+1)}}{(x+1)^2(x1)}+\frac{4\color{blue}{(x1)}}{(x+1)^2(x1)}\)

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1and that's the same as \(\Large \frac{5\color{red}{(x+1)}+4\color{blue}{(x1)}}{(x+1)^2(x1)}\)

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1Next step is to expand and simplify the numerator: \(\Large \frac{5x+5+4x4}{(x+1)^2(x1)}=\frac{9x+1}{(x+1)^2(x1)}\) and that's the end of the calculations.

pooja195
 one year ago
Best ResponseYou've already chosen the best response.1I read these but only half .. @mathmate

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1Did you understand as far as you read?

pooja195
 one year ago
Best ResponseYou've already chosen the best response.1yes but now we can start studying for the finals :P >_<

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1Here's the diagnostic test, as far as I have done. I will add other things on.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1ok, let's get started. Any questions on chapter 1?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1Say, 4^d=64, what is "d".

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1Just two rules: Anything raised to the power of 0 is 1, anything raised to the power of 1 is the base itself, like 4^1=4

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1Remember, \(4^2=4.4\), \(4^3=4.4.4\), \(4^4=4.4.4.4\), etc.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1compare 4^3=64, 4^d=64 so what is d? yes, d=3

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1Great! Now try 8=2^z. what is z?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1Good! Now a difficult one: \(3^2=\)?

pooja195
 one year ago
Best ResponseYou've already chosen the best response.19? or if its (3)^2 it would be 9

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1Exactly, that's where many students make mistakes. when in doubt, use PEMDAS which says that exponentiation goes before subtraction (negative), so what you did was correct. (3)^2 would raise the power of 3, so (3)*(3)=+9. Well done!

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1Try the following: 1^3= 3=3^j, j= 1=4^h, h= 3^r=81, r= (2)^3=

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1Laws of exponent: 2^n = 2.2.2.....2 (n times) \(a^m \times a^n = a^{m+n}\) \(\large a^{m}=\frac{1}{a^m}\) \(\large a^{\frac{1}{2}}=\sqrt a\) \(\Large a^{\frac{1}{2}}=\frac{1}{\sqrt a}\)

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1Now practice: \(\Large (\frac{1}{2})^2=\) \(\Large (0.2)^3=(\frac{2}{10})^3=(\frac{1}{5})^3=\frac{1}{125}\) Express \(\large 3^{8}\) with a positive exponent. \(\large 3^{8}\) =

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1dw:1433336557931:dw

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1Helps you see where numbers belong. R includes all numbers you're studying (i.e. does not include complex numbers) Inside of R is divided into Q (rational) and Q' (irrationals) Q' (irrationals) include numbers like sqrt(2), \(\pi\), sin(10\(^\circ \)), etc. Q (rationals) include \(all\) integers (Z), and all naturals (N). Decimals (2.5) repeating decimals (2.33333...), fractions (7/3) all belong to rationals, but not Z and N. All N belong to Z, but negative integers are in Z but not in N. See if you can read these relations from the diagram.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1Solve x+4<7 (page 324)

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1ok... too easy for you?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1Write an inequality to show the max. no. of apples I can buy if I have $4.8 and apples cost $0.60 each.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1* possible number of apples

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1I have $4.80, and apples cost 0.60 each. So the maximum number of apples I can buy is $4.80/0.60 =?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1Good, and the minimum?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1Well, the minimum would be zero. I don't have to buy any. So the answer would be:

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1That's the maximum number of apples. If we ask for the possible number, then it would be:

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1I can buy anything from 0 to 8, so \(\large 0\le x \le 8\), where x is the number of apples.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1Does that make sense?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1Excellent! now solve 5x+10=30

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1now solve \(5x+10\le30\)

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1Very good!!! you actually know the rules!

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1Why is it \(\ge\) and not \(\le\) ?

pooja195
 one year ago
Best ResponseYou've already chosen the best response.1because when you divide by a negative you always need to flip the signs

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1Excellent! What if you multiply by a negative?

pooja195
 one year ago
Best ResponseYou've already chosen the best response.1Keep the sign as it is DO NOT change it :)

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1Is x/(1) equal to x*(1)? why would the rule be different?

pooja195
 one year ago
Best ResponseYou've already chosen the best response.1idk its just like that ..

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1Actually, whether you multiply or divide by a negative, you flip the direction of the > or < sign. You can remember that precisely because x*(1) is the same as x/(1). So can you now solve

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1\(\Large \frac{5}{3}(x5)=6\)

pooja195
 one year ago
Best ResponseYou've already chosen the best response.1\[\frac{ 5 }{ 3 }x\frac{ 25 }{ 3 }=6\]

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1There is a trick to solving equations with fractional coefficients!

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1I would multiply by the denominator, or LCM of the denominator if there are many.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1This way, we end up with an equation with integer coefficients.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1\(\Large \frac{5}{3}(x5)=6\) \(\Large 3*\frac{5}{3}(x5)=3*6\) \(\Large 5(x5)=18\) and then go from here

pooja195
 one year ago
Best ResponseYou've already chosen the best response.1\[\huge~5x25=18\] \[\huge~5x=43\] \[\huge~x=\frac{ 43}{ 5 }\]

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1Any questions before we move on to linear equations?

pooja195
 one year ago
Best ResponseYou've already chosen the best response.1no, but lets skip graphing :/

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1You're willing to forfeit the points?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1What is a linear equation in slopeintercept form?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1Good! Can you find a line with a slope of 2 that passes through (2,4)?

pooja195
 one year ago
Best ResponseYou've already chosen the best response.1Point slope formula \[\huge~yy1=m(xx1)\] \[\huge~y4=2(x2)\] \[\huge~y4=2x4\] \[\huge~y=2x\]

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1Excellent. What form of equation did you use?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1I call it pointslope form. Not many school teach this form.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1Sorry, I didn't see it!

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1Now how about a line that passes through 2 points. Can you find it?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1The points are (2,5), (7,15)

pooja195
 one year ago
Best ResponseYou've already chosen the best response.1Find slope first \[\huge~\frac{ y2y1 }{ x2x1 }\] \[\huge~\frac{ 155 }{ 72}=\frac{ 10 }{ 5 }=5\] Point slope formula \[\huge~yy1=m(xx1)\] Pick a point right? \[\huge~y5=5(x2)\] \[\huge~y5=5x10\] \[\huge~y=5x5\]

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1you got 90% for this one!

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1All the steps are perfect, but 10/5=2 !!!!

pooja195
 one year ago
Best ResponseYou've already chosen the best response.1Are you going to make me redo all the work????? ;;

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1That's no problem. That's how I would correct, more for steps.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1If your steps are good, that's what's important.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1But do be careful in tests and exams.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1Translate into a mathematical inequality: Ken's age (k) is at least four years older than Pete's (p).

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1Great! It wasn't easy for you, but you did it!

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1Now try: Liz (L) has at least 4 times less flowers than Priya (P).

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1At least 4 times could mean 5 times!

pooja195
 one year ago
Best ResponseYou've already chosen the best response.1Idk know this one ..

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1When in doubt, put numbers in. Say Liz has $10, how much should Priya have?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1$40, $50, $60, anything $40 or more, right?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1Sorry, change flowers to $...:(

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1So if L=10, P=40, so we write \(\Large 4L \le P\)

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1That's what you would have done?

pooja195
 one year ago
Best ResponseYou've already chosen the best response.1i was thinking something similiar

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1Good. Be careful, many students would write L\(\le\) 4P.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1so using numbers, you can check your work.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1How are we doing so far?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1Pace? 1=too slow, 10=too fast.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1ok, we're on the right track.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1Gimme a minute, I have to flip the pages. You can go get a glass of water, you talked a lot! lol

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1Heard about compound inequalities? (6.5)

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1Have you done interval notation?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1Like (5,8(, or ]5, 8]

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1They are usually used to solve compound inequalities.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1Since you haven't done it, we'll describe by words.

pooja195
 one year ago
Best ResponseYou've already chosen the best response.1You mean and and or ?

pooja195
 one year ago
Best ResponseYou've already chosen the best response.1\[x+3<5~~or~~~5<x+3\]

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1Can you try to solve x<5 or x>4

pooja195
 one year ago
Best ResponseYou've already chosen the best response.1They are already solved. 

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1Change to and: Can you try to solve x<5 and x>4

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1No, I'll draw the number line.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1dw:1433387503479:dw

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1Solution for or is shown in the graph. But for and, there is no number that satisfies the and condition. No number can be less than 5 and greater than 4 at the same time, so answer is "no solution".

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1How about solving: x>4 and x<10 Use the number line if necessary

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1Feel free to show intermediate steps progressively. You don't have to wait till you typed up everything.

pooja195
 one year ago
Best ResponseYou've already chosen the best response.1dw:1433387789387:dw

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1The answer is correct graphically. How would you write it mathematically?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1You can write it as \(4\lt x\lt10\) whe it is a range

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1But be careful about the difference between \(\le\) and \(\lt\) etc

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1Moving onto 6.6 unless you have questions.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1Very good. I see that your book does not write the answer in set notation, for example: x={2,2}

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1Neither does your teacher?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1ok, no problem. Solve x<2

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1Again, these two "and" inequalities make a range between 2 and +2 so we write 2<x<2. ok?

pooja195
 one year ago
Best ResponseYou've already chosen the best response.1x−3=5 x=8 x−3=−5 x=2

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1So x=8 or 2 Good, you know your stuff! This is encouraging! what do you think?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1now solve 2x7 3=6

pooja195
 one year ago
Best ResponseYou've already chosen the best response.1add 3 to both sides 2x7=9 x=8 2x7=9 x=1

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1Very good! It's still easy?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1We move onto abs. inequalities.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1solve 43x 2 \(\le\) 7

pooja195
 one year ago
Best ResponseYou've already chosen the best response.1Do you want me to show the work?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1Not in this case, will save some time.

pooja195
 one year ago
Best ResponseYou've already chosen the best response.1\[\huge~x \ge \frac{ 5 }{ 3} ~~~and ~~~x \le \frac{ 13 }{ 3 }\]

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1Can you check if it is x>=13/3

pooja195
 one year ago
Best ResponseYou've already chosen the best response.1−3x+4−4≥−9−4 I subtracted 4 from both sides −3x≥−13 i divided and flipped the signs it should be \[\huge~\frac{ 13 }{ 3 }\]

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1I have 43x <= 9 (second case) 3x <= 13 3x >= 13 so x>=13/3 do you agree?

pooja195
 one year ago
Best ResponseYou've already chosen the best response.1oh right the negatives cancel

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1yes, they do (after flipping sign)

pooja195
 one year ago
Best ResponseYou've already chosen the best response.1and then u flipped ..

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1Looks like you're good till 6.7 (perhaps as you expected).

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1Sorry, didn't achieve 2 chapters, not even one, but we're efficient.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1If we have time later on, we may go back to word problems.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1Sure, we'll continue with 6.8 then.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1The NO is a telltale sign! :)

pooja195
 one year ago
Best ResponseYou've already chosen the best response.1\(\color{blue}{\text{Originally Posted by}}\) @mathmate If we have time later on, we may go back to word problems. \(\color{blue}{\text{End of Quote}}\) NONONONONONON!!!

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1Not today. Want to do word problems when you're fresh. We'll move on to graphics in 2 variables. p.367

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1Can you tell me in a few words about graphing linear inequalities in two variables?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1Use words like region, feasible, vertical, horizontal lines, etc
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