Question

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

Answer 1

If 6=2|x+6|-4
Then 10=2|x+6|
|x+6|=5
which means x+6=5 OR x+6=-5
so x=-1 OR x=-11

Answer 2

x= -1 or x= -11

Explanation:

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

To Find : value of x

Solution :

Since we are given that f(x)=6

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

⇒2|x+6|-4 =6

⇒2|x+6|=6+4

⇒2|x+6|=10

⇒
`|x+6|=(10)/(2)`

⇒
`|x+6|=5`

Now absolute mode : the absolute value or modulus |x| of a real number x is the non-negative value of x without regard to its sign. Namely, |x| = x for a positive x, |x| = −x for a negative x

⇒x+6=5 or x+6= -5

⇒x=5-6 or x= -5-6

⇒x= -1 or x= -11

Thus for x = -1 or x =-11 , f(x) =6