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?
a)x + 2 = −4
b)−x − 2 = 4
c)x + 2 = 4
d)x − 2 = −4

Answer 1

The correct next step to solve the equation |x − 2| = 4 is x − 2 = −4.

Step-by-step explanation:

The correct next step to solve the equation |x − 2| = 4 is option d) x − 2 = −4.

To solve the equation, we need to isolate x. Since we have the absolute value of x − 2 equal to a positive number, we have two possible cases: x − 2 = 4 and x − 2 = -4. By solving the equations, we find that x = 6 or x = -2.

Therefore, option d) x − 2 = −4 is the correct next step to solve the equation.