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anonymous
 5 years ago
Explain, please:
x < a means x < a or x < a
x < a means a < x and x > a
or we say a < x < a is same as x < a
anonymous
 5 years ago
Explain, please: x < a means x < a or x < a x < a means a < x and x > a or we say a < x < a is same as x < a

This Question is Closed

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0x means the absolute value of x, or the distance of x away from 0. Therefore, if x<0, x returns x if x > 0 , x returns x

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0ok but i must compare the two hamburgers by comparing the volume of the beef in each burger. the volume V of a burger is V= Ah, whee A is the area and h is the height. the area of the lite burger is nr^2, where r is the radius (half the distance across the middle) of the burger. for the lite burger, r= 2 inches, so its area is

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0In other words or at least more words: positive numbers return themselves negative numbers turn positive \[\left 2 \right = 2 and \left 2 \right = 2\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Thank you, I understand that. But then how come for a question like this 5x 2 < 4 has two answers, x < 6/5 or x > 2/5 ?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0This is easier to see on a number line so let me try something easier x > 4 the answer is x<4 or x>4.... does it make sense that you have to go more than 4 units away from zero in either direction because the  symbols ignore positive/negative?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0who says 5x2<4 has two answers (solutions)? first of all there are an infinite number of solutions, but they are contained in one interval. the interval is 2/5 < x < 6/5 which is an AND statement: x is greater than 2/5 and less than 6/5

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Oh okay, I understand that now. But then how do we define whether x is > or < ? This is my initial question, maybe before I was framing it wrong.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0let me give you a simple example. start with  x 1  < 2. this says x is within 2 units of 1. so if you draw a number line you can see you can go up to three and down to 1, so the solution is 1 < x < 3

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0wheres if we say  x  1 > 2 this means x is greater than two units from 1. so we can be below 1 or above 3. the answer is therefore two intervals, all numbers less than 1 or all numbers greater than 3. you have to write two intervals: x < 1 or x > 3

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0if you draw a number line you can see it easily.  x  a  < b will be one interval (assuming b is greater than or equal to zero, otherwise it makes no sense) and  x  a  > b will be two intervals.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0it is really not that complicated if you remember that  x  a  is the distance between x and a. so if i am on a highway that runs east west (like the number line) and I say i am within 5 miles from mile marker 100, that means i must be somewhere between mile marker 95 and mile marker 105. i.e. the solution to  x  100  < 5 is 95 < x < 105 but if i say i am further than 5 miles from mile marker 100 i must be either east of marker 105 or west of marker 95 i.e. x 100 > 5 means x < 95 or x > 105

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I understand this too. But when it comes to complex questions, I get confused. Like for example: 13x > 8. So in the solution set, how do we determine that x is < 7/3 and x > 3 when we started with 13x >8 and 13x < 8 respectively?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0ok first of all i hope it is clear that 13x = 3x1 try it with numbers, or just know that ab=ba

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so there is no difference between solving 13x>8 and 3x1>8

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0second of all, as for my example above, you know that if you are solving xa<b you will have one interval (not one solution) and if you have  x  a > b you will have two solutions.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0and something they often forget to mention is that there is really know difference between solving x  a < b and x  a  > b after all, if i know one i know the other. for example if the solution to x  a < b is 5 < x < 10 then i know the solution to x  a> b is x < 5 or x > 10 after all those are the logical choices right? either greater than or less than.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so how would i solve 13x> 8 ? first of all i hate having to remember to switch the inequality when dividing by a negative number so i would rewrite it as 3x1>8

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0then i have a choice. i could solve 3x1< 8 and take everything else, like this: 8 < 3x 1 < 8 7 < 3x < 9 7/3 < x < 3 and that is exactly what i don't want so i say x < 7/3 or x > 3

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0or i could do what they teach you and say 3x  1> 8 means two intervals (we know that) therefore two inequalities to start: 3x1< 8 or 3x  1 > 8 and solve these separately. 3x 1 < 8 3x < 7 x < 7/3 OR 3x1 > 8 3x > 9 x > 3 either way you need to know when you will have one interval (compound inequality) or two

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0(just to be sure) ..and that is when xa < b there will be one interval and when xa > b two intervals?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yes exactly. if you can remember that you will be in good shape

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0thank you so much. this explains much better!

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.05x+17>9 two intervals 3x+7<12 on interval

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0and while i have your attention one more thing" Like for example: 13x > 8. So in the solution set, how do we determine that x is < 7/3 and x > 3 when we started with 13x >8 and 13x < 8 respectively? in this sentence your "ands" should be "OR"s x < 2 OR x > 7 there is not such thing as x < 2 and x > 7
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