## cookiemonster2412 one year ago I need help with absolute value equations!

1. anonymous

$\left| 6x+7 \right|=5x+2$

3. anonymous

hold on

4. anonymous

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

I need it to be explained.

6. 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.

7. anonymous

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

8. 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

9. phi

*either6x+7 is positive or negative

10. anonymous

And it is positive.

11. phi

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

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

13. phi

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

x=-5

15. 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 $\left| 6x+7 \right|=5x+2 \\ |-23|= 5\cdot -5+2 \\ 23= -23 \text{ NO!}$

16. 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 $-1\cdot (6x+7) = 5x+2$

x= -9/11

18. 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

How do I graph this?

20. phi

can you plot y=5x+2 ?

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

22. phi

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

All it says is to solve and graph the equation.

24. phi

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

I'm sure.

26. phi

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