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?

x + 2 = -4

-x - 2 = 4

x + 2 = 4

x - 2 = -4

Answer 1

@jigglypuff314

Answer 2

x - 2 = -4 is the next step. When solving absolute value problems you need to take into account that what is inside the absolute value symbols can be negative or positive. What is in the symbols does not change, you just take into consideration that you can take the absolute value of either the negative or positive of a number. Similar to taking the square root of a number, you can square either -5 or 5 and get 25, but the square root of 25 can be either 5 or -5.