Question

If |14 −2x| = 20, x could equal which of the following?

a. −3 only
b. 3 only
c. −3 or 3 only
d. −3 or 17 only
e. 3 or 17 only

Answer 1

Solving the absolute value equation gives two possible values for x: -3 and 17. Therefore, the correct answer is d. −3 or 17 only.

Step-by-step explanation:

The student asked: If |14 − 2x| = 20, x could equal which of the following?

To solve |14 − 2x| = 20, we consider the two possible cases for absolute value equations:

1. Case 1: The inside of the absolute value is positive, so we can write 14 - 2x = 20.

• Subtract 14 from both sides to get -2x = 6.
• Divide both sides by -2 to get x = -3.
• Therefore, x could equal -3.

1. Case 2: The inside of the absolute value is negative, and thus we write 14 - 2x = -20.

• Subtract 14 from both sides to get -2x = -34.
• Divide both sides by -2 to get x = 17.
• Therefore, x could also equal 17.

The correct answer is thus x could equal −3 or 17 only.

Therefore, the correct choice is d. −3 or 17 only.