Question

3. (02.03 MC)

Solve for x: |3x + 12| = 18 (5 points)
x = 2, x = -10
x = 2, x = -2
x = 10, x = -10
x = -2, x = 10

Answer 1

the answer is x = 2.

Answer 2

the 2 solutions are
`x=2` and
`x=-10`

Explanation:

absolute value bars are tricky, they make whatever is inside positive regardless of if it is positive or negative

basically, |x|=|-x|

or |-3|=|3|=3

so one way to solve this is to solve the 2 cases: one where it is positive and one where it is negative

solve these 2 cases:

case1: positive: 3x+12=+18

case2: negative: 3x+12=-18

case1:

`3x+12=18`

minus 12 both sides

`3x=6`

divide both sides by 3

`x=2` is one solution

case2:

`3x+12=-18`

minus 12 both sides

`3x=-30`

divide both sides by 3

`x=-10` is the other solution

the 2 solutions are
`x=2` and
`x=-10`