Question

Given g(x)=|-3x+16|, if g(x)=18, find x.

Answer 1

Given:-

g(x)=18

To find:-

x

Solution:-

g(x)=(-3x+16)

18=-3x+16

18-16=-3x

2=-3x

x=2/-3

hope it helps you!

Answer 2

x = -
`(2)/(3)` , x =
`(34)/(3)`

Explanation:

The absolute value function always gives a positive value, however, the expression inside can be positive or negative, that is

- 3x + 16 = 18 or -(- 3x + 16) = 18

Solving

- 3x + 16 = 18 ( subtract 16 from both sides )

- 3x = 2 ( divide both sides by - 3 )

x = -
`(2)/(3)`

or

-(- 3x + 16) = 18

3x - 16 = 18 ( add 16 to both sides )

3x = 34 ( divide both sides by 3 )

x =
`(34)/(4)`

As a check

Substitute these values into the left side of the equation and if equal to the right side then they are the solutions.

| - 3(-
`(2)/(3)` ) + 16 | = | 2 + 16 | = | 18 | = 18 ← True

| - 3(
`(34)/(3)` ) + 16 | = | - 34 + 16 | = | - 18 | = 18 ← True

Thus x = -
`(2)/(3)` and x =
`(34)/(3)` are the solutions