Question

Solve for all possible values of x: |x-18| = 5

Answer 1

The equation |x-18| = 5 has two possible solutions. By considering the definition of absolute value, we find that the possible values for x are 13 and 23.

Step-by-step explanation:

To solve the equation |x-18| = 5, we need to consider the definition of absolute value, which states that |a| = a if a ≥ 0, and |a| = -a if a < 0. Therefore, the equation |x-18| = 5 has two possible cases:

1. x - 18 = 5
2. x - 18 = -5

For the first case:

x - 18 = 5
x = 5 + 18
x = 23

For the second case:

x - 18 = -5
x = -5 + 18
x = 13

Thus, the two possible values of x are 13 and 23.