Question

(2.03)

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? (1 point)

Answer 1

Given the definition of the absolute value function, there are two possibilities for the next step.

Rember that |x| = x when x is positive and |x| is - x when x is negative.

So, these are the two possibilities for |x - 2| = 4

1) When the content inside the absolute value is positive, you can state x - 2 = 4

2) When the content inside the absolute value is negative you can state x - 2 = - 4.

So, the answer is

x - 2 = 4 and x - 2 = - 4.

I found this list of choices for this question:

a. x + 2 = −4
b. −x − 2 = 4
c. x + 2 = 4
d. x − 2 = −4

In that list , the only right is x - 2 = - 4, so choose it.

Answer: option d. x - 2 = - 4