Please help me to understand and solve these!

- Faman39

Please help me to understand and solve these!

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- Faman39

##### 1 Attachment

- Faman39

@mathmate can you able to help me with this?

- mathmate

DId you work out the solutions to each of the inequalities?

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## More answers

- Faman39

I didnt understand completely those problem, thats y

- mathmate

Solve them as equations, and since they are <, so you need any answer that is smaller the equality.

- Faman39

I cant really get it how to do it, but i did somehow, where i got half n half write. I need to understand whole n how to find the rite answer

- mathmate

The questions are all inequalities.
Say you solve the first one as an equality:
-2(1+z)+5z+5<11
-2-2z+4z+5<11
2z<11-3=8, or
z<4
So any of the answers will fit for #1.
Now proceed with #2, #3, #4
and try to move a,b,c,d around so that ALL the inequalities are satisfied.

- Faman39

cqn you wait, cuz i m gonna show you those.

- Faman39

First one will fit on which one, would it be 2

- mathmate

Because they are not equations, but inequalities, you are better of doing all 4 of them before fitting anything. For example, all the answers a,b,c,d will fit in the first. So you don't know which one to choose until you have all 4 inequalities solved.

- mathmate

Note: inequalities have multiple answers.

- Faman39

So but i want to how will i get this answer matching correct answer

- Faman39

Of all of them

- mathmate

Let say if you have a set of answers 1,3,5,7
and solutions to equations which are
x<2,x<6,x<8,x<4
Then your choice would be to fit 1<2, 5<6, 7<8,3<4, or else you would have one left over such as:
1<2,3<6,5<8, but 7>4 will not work.
That's why you need to work out all four before you can match.

- Faman39

Ok so, -2 (1 + z) +4z +5 <11
-2 + -2z + 4z + 5 <11
-2 + 2z + 5<11
so does it mean 2 will match or no?

- mathmate

You have to solve it completely,
-2+2z+5<11
2z+3<11
2z<8
z<4
Now you still have to solve the other three before you can start matching.

- Faman39

that 2 match with this one right?

- mathmate

All four answers will match with this one. If you want to take a chance, choose the highest number that will match. But I suggest you work out ALL 4 inequalities, then match. That will be much more sure.

- mathmate

all four will match, because
3<4
-3<4
2<4
0<4
. That is why I suggest you work out all four inequalities before matching.

- Faman39

All does not matched up, thats y, i m asking, how will i figure out all this

- mathmate

If you want, you can pick 2<4.
If you choose now, the rest may or may not work.

- mathmate

1. Solve all FOUR inequalities, so you have 4 inequalities in hand, such as
z<4
z< ?
z< ?
z< ?
2. Match the 4 given answers so that EVERY inequality works.

- Faman39

Second will be -3, am i right?

- mathmate

I'm afraid not. You have a problem with the sign.

- mathmate

...unless you mean -z>-3

- Faman39

I was saying according that table which i showed

- Faman39

So it suppose to match up with b -3

- Faman39

right?

- mathmate

Inequalities are not equations. Solutions must remain inequalities.
So the second one must be given in the form z<-3, or z>3, or z<3.
-3 would not be the solution to an inequality.
Can you show your work?

- Faman39

ok

- Faman39

3z - 5z +10 - 8 <6

- mathmate

3z - 5z +10 - 8 does not look right. Can you check?

- Faman39

2z + 10 - 8 <6
so if this be 2, then other was not 2

- Faman39

I cant really know how to do these all

- Faman39

Problems seems really confusing to me

- mathmate

3z - 5z +10 - 8 <6
is inorrect. it should be +5z and -10. How did you get the signs reversed?

- mathmate

Or written in full
3z+5z-10-8<6

- Faman39

so your saying it would match up with 3, right?

- Faman39

Thats how we find the 3

- mathmate

You are going to far with matching.
You need to solve ALL 4 inequalities before you can match.
the answer to the second is then....?

- mathmate

I mean the \(solution\) to the second inequality is then....?

- Faman39

I dont get at all how to last four, thats y i put their answer by guess, i m sure those last two were wrong but there is two matching which i gave, it was correct

- mathmate

If you don't need all four correct, that's ok. Go ahead and do it your way. I have no problem with that. Good luck with your guesses. :)

- mathmate

In mathematics, you are allowed to guess, but you also need a way to check your answer. If you cannot do both, then, sorry, guessing is not the right way.

- Faman39

Thank you but all i wanted to know how to solve these, i havent done all by guess just two one which mite, but um not sure abt how to solve it to find exact answer to match. I just want to be clear abt all this

- Faman39

I m not getting to find all of it exact answer

- mathmate

I repeat:
1. Solve ALL four inequalities in the form
z<4
z<3
z< ?
z< /
2. THEN match the inequalities with the 4 given answers to make sure ALL inequalities are satisfied.
I am still waiting for the solution to the second inequality after I have done the first one.
If you have problems solving inequalities, that's where you need to work on.

- Faman39

3z - 10 + 5z - 8 <6
3z + 5z + 10 - 8 <6
8z + 2<6

- Faman39

8z + 2 - 2 <6
8z <6

- Faman39

it will be a 0?

- Faman39

No

- Faman39

Please help!

- Faman39

I dont understand how to solve all this

- Faman39

@CalebBeavers help me please

- Faman39

@phi

- Faman39

Thank you so much for helping tolerating pain like me, i m sorry so for trouble. I really appreciate your help @mathmate, thanks alot! :)

- Faman39

This one @experimentX

- experimentX

first of all simplify the left side. Can you simplify
\[ -2(1+z) + 4z + 5\]

- Faman39

-2z + -2z + 4z +5
4z +4z +5
8z +5

- Faman39

isnt it?

- experimentX

nope!!

- experimentX

\[ -2(1+z) = (-2) \times 1 + (-2) \times z = ?\]

- Faman39

-2 +2z = -2 (-2) X z =
-2 + 2z = -4 X z
I m stuck :( sorry

- Faman39

-2

- experimentX

\[ -2 \times z = ?\]

- Faman39

-2z

- experimentX

-2 + (-2z)= ?

- Faman39

4z?

- experimentX

no ... you cannot add like that.

- experimentX

|dw:1358353383731:dw|

- experimentX

do you know how to take common?

- Faman39

3x + 3x

- experimentX

|dw:1358353592998:dw|

- Faman39

5x

- experimentX

yes!!

- experimentX

1$ + 2$ = 3$
1$ + 2 pound = 3$
------------------
which of above is correct?

- Faman39

3?

- Faman39

both are same

- experimentX

what is the name of your currency?

- Faman39

pound

- experimentX

okay .. is
1 dollar + 2 pound = 3 dollar ?

- Faman39

no

- experimentX

is that correct?

- Faman39

no

- experimentX

why not?

- Faman39

Both are not similar

- experimentX

yep!!
-2 + (-2z)
here think of z as dollar and ... ther is nothing after -2 ... think of it as there is pound.

- Faman39

So what i did on all that problems, so how do i match because, its seems tricky

- experimentX

also I think there is no minus there. your first problem is
\[ 2(1+z) + 4z+5 = ?\]
Simplify this.
thikn of \( 4z + 5\) as .. 4 dollar + 5 pound

- Faman39

it cannot be added

- Faman39

so the bracket one what we need to do

- experimentX

at least you can make it a bit simpler.

- Faman39

-2 + 2z +4z +5
- 2 + 6z +5

- Faman39

?

- experimentX

quite not correct.
+ ( - 2z) = ?

- experimentX

no ...
|dw:1358354499867:dw|

- Faman39

-2z

- Faman39

so 2 match up with this?

- Faman39

I meant, first problem

- experimentX

okay now simplify the first problem.

- Faman39

-2z + 5 < 11

- Faman39

-2z < 6

- Faman39

z < 6/-2
z < -3

- Faman39

it is match up with b

- experimentX

No ... you didn't do it correctly.

- Faman39

divide both side

- Faman39

right?

- Faman39

i forgot, just did one side directly

- experimentX

woops!! sorry ... your first problem.
\[ -2(1+z) + 4z+5 = -(2(1+z)) + 4z+5 = -(2\times 1 + 2 \times z) + 4z + 5 \\
= -(2 + 2z) + 4z+5 = -2 - 2z + 4z+5 = (-2z+4z) + (-2+5) = 2z + 3\]

- experimentX

do you understand the each step?

- Faman39

but am i right with first one?

- experimentX

did you get 2z+3?

- Faman39

no i got -3

- experimentX

2z+3 < 11
2z+3 - 3 < 11 - 3
2z . (1/2) < 8/2 = 4
http://www.wolframalpha.com/input/?i=-2%281%2Bz%29+%2B+4z%2B5+%3C%3D+11

- experimentX

if you had done it correctly ... you should have got
\[ z < 4 \]

- Faman39

you are saying it match up 3

- Faman39

right?

- experimentX

yes
copy these each step into your notebook and see if you understand each of these steps
\[
\begin{align*}
-2(1+z) + 4z+5 &= -2(1+z) + 4z+5 \\
&= -2(1+z) + 4z+5 \\
&= -(2(1+z)) + 4z+5 \\
&= -(2\times 1 + 2 \times z) + 4z + 5 \\
&= -(2 + 2z) + 4z+5 \\
&= -2 - 2z + 4z+5 \\
&= (-2z+4z) + (-2+5) \\
&= 2z + 3
\end{align*} \]

- Faman39

thank you :) it making sense now

- Faman39

thank you so much

- experimentX

also if you have any misunderstanding ... don't hesitate to ask.

- Faman39

can you show me other 3, if your not busy or if i didnt eaten up your head, i know i m painful, i hardly understand everything in math

- Faman39

thats really horrible

- experimentX

first simplify do 2nd and 4 th problem

- experimentX

i think you are capable to do it .. also show me step!!

- Faman39

3z + 5z - 10 - 8 < 6?

- experimentX

yes go on!!

- Faman39

8z - 10 - 8 <6
8z - 2 <6
8z <6 +2
8z < 8
z < 0

- experimentX

http://www.wolframalpha.com/input/?i=3z+%2B+5z+-+10+-+8+%3C+6
watch your second step again.

- Faman39

Sorry so, 8z - 18 < 6
8z < 6 - 18
8z < 12
1.5? :(

- experimentX

8z - 18 < 6
add +18 to both sides.

- Faman39

8z < 24
<3

- experimentX

yes correct!!
do the 4th problem similarly ...
also note the mistake you made
Sorry so, 8z - 18 < 6
8z < 6 - 18
8z < 12 (is 6-18 = 12 ??)
1.5? :(
Get calculator. or watch your step agai.

- Faman39

In third one, how do i start?

- experimentX

watch the example i gave you!!

- Faman39

I m so sorry, i m such a error maker, pls forgive me for all this trouble

- experimentX

in which level do you study?

- Faman39

no actually im in online high school, where i m takin blended course

- experimentX

really? you got terrible math!! these are very very basic simple rules

- Faman39

yes, im ok with other but worse in math

- experimentX

okay try 3

- experimentX

what did you put on 2?

- Faman39

Z + 5 - ( 1 + 6z) > -1

- Faman39

z +5 - 1 + 6z > -1

- experimentX

there you have problem!!
-(1+6z) = -1 times .. what's inside

- experimentX

|dw:1358357567000:dw|

- Faman39

-1 + -6z

- experimentX

what is + - 6z = ?

- Faman39

- 6z

- experimentX

yes ... now simplify it

- Faman39

7z

- experimentX

again, you are not getting the point. look at the big picture. look again from where you started and where you ended. and check for errors.

- Faman39

ok sorry

- Faman39

z + 5 - -1 + -6z <1

- experimentX

it's necessary that you write the whole step on some nontebook.

- experimentX

*notebook ... if you rely on memory then you will never learn.
also it's necessary that you have to look at your previous step.

- Faman39

ok sure, i will keep it mind. z + -6z + 5- + -1
5z + 6 < 1

- Faman39

I know, something wrong in here again

- Faman39

5z < 1 - 6
5z < 5
1

- Faman39

<1

- Faman39

am i wrong?

- experimentX

try pluggin that expression on Wolfram Alpha

- Faman39

I dont know how to do it

- Faman39

:(

- Faman39

your saying negative

- experimentX

how do you do with this
\[ a + 2b - (3a+b) = a + 2b - 3a -b = a-3a+2b-b = -2a +b \]

- Faman39

add by combining like term

- experimentX

how did i get rid of -(3a+b) .. just do it like there.

- Faman39

- 3a + b, we cant go more from this on it

- experimentX

- 3a - b

- experimentX

|dw:1358359171654:dw|

- Faman39

so then your saying it will move to positive

- Faman39

But i didnt understand how did operation + to - at middle

- Faman39

Hows did you change and why?

- experimentX

no ... |dw:1358359302646:dw|

- Faman39

ok

- experimentX

|dw:1358359471738:dw|

- Faman39

not equal

- Faman39

yes

- Faman39

you multiplied - all on Bracket, thats y, everything -

- experimentX

|dw:1358359803427:dw|

- Faman39

- 3a + -2b

- experimentX

tell me in terms of pounds and dollars .... how much should you give to me?

- Faman39

3 dollar, 2 pounds

- experimentX

isn't that equal to -3a-2b? what does this mean?

- experimentX

|dw:1358360151961:dw|

- experimentX

|dw:1358360292451:dw|

- experimentX

|dw:1358360405299:dw||dw:1358360432011:dw|

- Faman39

got it now :) thank you

- Faman39

thats y it was - 1, right

- experimentX

Honestly, I feel like you are trolling with me!!
right ... do the third number now and show it to me.

- Faman39

I m extremely sorry for taking your time n making you crazy like this

- Faman39

:( i m so sorry for everything

- Faman39

- 7z - 19 + 19 < 5 +19
-7z + < 24
got long decimal number

- experimentX

you copied the wrong question.
- 7z - 19 + 19 < -5 +19

- Faman39

so first one was right ?

- Faman39

which i showed you b4

- experimentX

no you had +7z ...

- Faman39

-8z - 19 + z > - 5

- Faman39

so -7z + 19 < 5
- 7z + 19 - 19 < 5-19
-7z < 14
z < -2

- experimentX

well ... done!!
gotta go ... i strongly suggest that you get a pencil and notebook and practice few similar problems.

- Faman39

Thank you so much! im sorry again for trouble :(

- experimentX

I am not in trouble ,,, you might be in math test!! so pratice well!!

- Faman39

yes, i was trying understand these so that i dont make mistake again like this

- Faman39

Last one match up with 2, right, just to be confirmed

- Faman39

i m extremely apologize for giving you trouble @experimentX. thank you so much for helping me alot! you really saved me explaining all of it. I m really very sorry horribly troubling you

- Faman39

You are really amazing, thank you so much for make me understand abt all of it without being tired. your truly great, thanks alot @experimentX

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