Given the function f(x) = 4|x - 5| + 3, for what values of x is, f(x) = 15?

Solution:

Given: Function f(x) = 4|x - 5| + 3 and f(x) = 15

We know that mod |x| = x for x > 0 and -x for x < 0

f(x) = 4|x - 5| + 3

Case(1): when f(x) = 4(x - 5) + 3

We have f(x) = 15

⇒ 4(x - 5) + 3 = 15

⇒ 4(x - 5) = 15 - 3 = 12

⇒ x - 5 = 12/4 = 3

⇒ x = 3 + 5 = 8

⇒ x = 8

Case(2): when f(x) = -4(x - 5) + 3

We have f(x) = 15

⇒ -4(x - 5) + 3 = 15

⇒ -4(x - 5) = 15 - 3 = 12

⇒ x - 5 = 12/-4 = -3

⇒ x= -3 + 5 = 2

⇒ x = 2

Therefore, the values of x are 8 and 2

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Given the function f(x) = 4|x - 5| + 3, for what values of x is, f(x) = 15?

Summary:

If the function f(x) = 4|x - 5| + 3, the values of x are 8 and 2 if f(x) = 15.