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## deboragranja one year ago What is the solution set for |–2x + 16| – 9 = –3

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1. Compassionate

Hello, you first want to solve the equation for x. Can you do that for me, hun?

2. deboragranja

x=11

3. Compassionate

There you go ;)

4. deboragranja

thats the answer to the entire thing?

5. genius12

nope there is 2 answers.

6. deboragranja

11 and -11 right?

7. genius12

nope.

8. Compassionate

No. It's actually 11 and 5. Do you know why?

9. deboragranja

okay help me idk why

10. genius12

$\bf |-2x+16|=6 \implies -2x+16=6 \ or \ -2x+16=-6$

11. genius12

You have to cases to solve for. Since it's an absolute value, the answer could be +6 or -6 but either way it would come out as 6. So we consider both cases and solve for x in each case. We get x = 5 and x = 11.

12. deboragranja

ohhhhh okay thank you i get it.

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