- cookiemonster2412

I need help with absolute value equations!

- schrodinger

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- anonymous

whats your question

- cookiemonster2412

\[\left| 6x+7 \right|=5x+2\]

- anonymous

hold on

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## More answers

- anonymous

go to to mathway.com it gives u all s
ure answers k?

- cookiemonster2412

I need it to be explained.

- anonymous

Okay, absolute value is never a negative. For example, -5's absolute value would be 5.
Or -2's absolute value would be 2. http://www.purplemath.com/modules/absolute.htm
This site should help on absolute value.

- anonymous

The first part is asking you to find the absolute value of 6x+7.

- phi

when doing this
\[ \left| 6x+7 \right|=5x+2 \]
either 5x+7 is positive or negative
if it is zero or positive, we can drop the | | (they don't do anything)
so step 1: solve
6x+7 = 5x+2

- phi

*either6x+7 is positive or negative

- anonymous

And it is positive.

- phi

can you solve for x in
6x+7 = 5x+2 ?

- cookiemonster2412

This is what I got.
6x+7=5x+2 or 6x+7=5x-2

- phi

just
6x+7=5x+2
add -5x to both sides
add -7 to both sides

- cookiemonster2412

x=-5

- phi

now we check to see if that works
6x+7 with x= -5
6*-5+7 = -30+7 = -23
we assumed it was positive but we got a negative answer. not good
but if we continue and check the other side
\[ \left| 6x+7 \right|=5x+2 \\
|-23|= 5\cdot -5+2 \\
23= -23 \text{ NO!}
\]

- phi

now let's assume 6x+7 is negative
if it is negative, then -1*(6x+7) will be positive
so | 6x+7| is the same as -1*(6x+7) (both become positive)
so let's solve
\[ -1\cdot (6x+7) = 5x+2\]

- cookiemonster2412

x= -9/11

- phi

yes, and now we check this one
6x+7= 6*-9/11 + 7 = -54/11 + 77/11 = 23/11
5x+2 = 5*-9/11 + 22/11 = -45/11 + 22/11 = -23/11
we end up with
23/11 = -23/11 and that is not true.
so there are no solutions for this problem

- cookiemonster2412

How do I graph this?

- phi

can you plot y=5x+2 ?

- cookiemonster2412

I'm supposed to graph it on a number line.

- phi

First, are you sure we have the correct problem? can you double check?

- cookiemonster2412

All it says is to solve and graph the equation.

- phi

yes, but are you sure it is
| 6x+7| = 5x+2

- cookiemonster2412

I'm sure.

- phi

in that case, there is no solution
you can't graph "no solution"
you can say there is none.

- cookiemonster2412

Okay. Thank you.

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