Given the function f(x) = 0.5|x - 4| - 3, for what values of x is f(x) = 7?

Solution:

f(x) = 0.5|x - 4| - 3 [Given]

7 = 0.5|x - 4| - 3

By adding 3 on both sides

0.5|x - 4| - 3 + 3 = 7 + 3

0.5|x - 4| = 10

Solve the equation by separating the variable x

Divide both sides by 0.5

|x - 4| = 20

So we get

x - 4 = 20 and x - 4 = - 20 (we get two values being an absolute value function)

Adding 4 on both sides

x - 4 + 4 = 20 + 4 and x - 4 + 4 = - 20 + 4

By further calculation

x = 24 and x = - 16

Therefore, the values of x are 24 and - 16.

Given the function f(x) = 0.5|x - 4| - 3, for what values of x is f(x) = 7?

Summary:

Given the function f(x) = 0.5|x - 4| - 3, the values of x are 24 and - 16 for f(x) = 7.