Question

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?

h 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

http://www.purplemath.com/modules/solveabs.htm
There are two possible answers. The next step would require removing the absolute value bars and creating two equations. Only one of those is a choice here.

Answer 2

Solve | x + 2 | = 7
To clear the absolute-value bars, I must split the equation into its two possible two cases, one case for each sign:

(x + 2) = 7 or –(x + 2) = 7
x + 2 = 7 or –x – 2 = 7
x = 5 or –9 = x