given the function $f(x)=2|x + 6|-4$, for what values of $x$ is $f(x)=6$?\n$x=-1,x = 11$\n$x=-1,x=-11$\n$x =…
given the function $f(x)=2|x + 6|-4$, for what values of $x$ is $f(x)=6$?\n$x=-1,x = 11$\n$x=-1,x=-11$\n$x = 14,x=-26$\n$x = 26,x=-14$
Answer
Explanation:
Step1: Set up the equation
Set (f(x) = 6), so (2|x + 6|-4=6).
Step2: Isolate the absolute - value term
Add 4 to both sides of the equation: (2|x + 6|=6 + 4), which simplifies to (2|x + 6|=10). Then divide both sides by 2: (|x + 6| = 5).
Step3: Solve for two cases
Case 1: (x+6 = 5). Subtract 6 from both sides: (x=5 - 6=-1). Case 2: (x + 6=-5). Subtract 6 from both sides: (x=-5 - 6=-11).
Answer:
(x=-1,x = - 11)