Answer:
[tex]x = - 1\: or \: x = - 11[/tex]
Step-by-step explanation:
The given function is
[tex]f(x) = 2 |x + 6| - 4[/tex]
We want to find the value of x, for which f(x) =6.
Let use equate the function to 6 and solve for x.
[tex] 2 |x + 6| - 4 = 6[/tex]
Add 4 to both sides to get:
[tex]2 |x + 6| = 6 + 4 \\ 2 |x + 6| = 10[/tex]
Divide through by 2 to get:
[tex]|x + 6| = 5[/tex]
Use the absolute value function definition to get:
[tex]x + 6 = 5 \: or \: x + 6= - 5[/tex]
Subbtract 6 from both sides to get:
[tex]x = 5 - 6\: or \: x = - 5 - 6[/tex]
[tex]x = - 1 \: or \: x = - 11[/tex]
