Given the function f (x) = 2|x + 6| - 4, fut what values of x is f (x) = 6?

-1 and - 11

Step-by-step explanation:

f (x) = 2|x + 6| - 4

Let f (x) = 6 and solve for x.

2|x + 6| - 4 = 6

Add 4 to both sides.

2|x + 6| = 10

Divide both sides by 2.

|x + 6| = 5

To deal with the absolute value in the equation we follow the rule below:

To solve an absolute value equation of the form |X| = k, where X is an expression in x, and k is a non-negative number, we solve the compound equation "X = k or X = - k".

x + 6 = 5 or x + 6 = - 5

Subtract 6 from both sides in both equations.

x = - 1 or x = - 11