Answer:
[tex]x = -1[/tex] or [tex]x = -11[/tex]
Step-by-step explanation:
Given
[tex]f(x) = 2|x+6| - 4[/tex]
Required
Find x when
[tex]f(x) = 6[/tex]
Substitute 6 for f(x)
[tex]6 = 2|x+6| - 4[/tex]
Add 4 to both sides
[tex]4+6 = 2|x+6| - 4+4[/tex]
[tex]10 = 2|x+6|[/tex]
Divide both sides by 2
[tex]5 = |x + 6|[/tex]
Rewrite as:
[tex]|x + 6| = 5[/tex]
This can be split to:
[tex]x + 6 = 5[/tex] or [tex]-(x + 6)=5[/tex]
Solve for x in both cases
[tex]x = 5 - 6[/tex] or [tex]x + 6 = -5[/tex]
[tex]x = -1[/tex] or [tex]x = -6 - 5[/tex]
[tex]x = -1[/tex] or [tex]x = -11[/tex]
