Question

HI EVERYONE!!
Below are the steps to solve an equation:

Step 1: |x - 2| + 3 = 7
Step 2: |x - 2| = 7 - 3
Step 3: |x - 2| = 4

Which of the following is a correct next step to solve the equation?
A) x + 2 = -4
B) -x - 2 = 4
C) x + 2 = 4
D) x - 2 = -4

Answer 1

please you have to consider two distinct cases, namely:
\[x-2\ge 0, x-2=4\]
and:
\[x-2<0,-x+2=4\]

Answer 2

what is your choice?

Answer 3

just open \[\left| x-2 \right|\]

Answer 4

please I rewrite:
case 1)
\[x-2\ge 0\]
then your equation can be rewritten as below:
\[x-2=4\]
case 2) \[x-2< 0\]
then your equation can be rewritten as below:
\[-x+2=4\]

Answer 5

exactly

Answer 6

@M_A thanks!

Answer 7

@kelliegirl33 @Michele_Laino @M_A Thank you all for your time and efforts.

Answer 8

its either :
(x - 2) = 4
OR
-(x - 2) = 4

Answer 9

@extremearianna thank you!

Answer 10

@kelliegirl33 what happened to the other comment? I thought it might have been D

Answer 11

your answer is D

Answer 12

Thank you very much! I will fan you also :)
@Michele_Laino

Answer 13

Thank you again!