Solve for x: |3x|=12

x = 4; x = - 4

Step-by-step explanation:

|3x| = 12

3x = 12

3x/3 = 12/3

x = 4

3x = - 12

3x/3 = - 12/3

x = - 4

Clear the absolute-value bars by splitting the equation into its two cases, one for the Positive case and the other for the Negative case.

The Absolute Value term is |x-3|

For the Negative case we'll use - (x-3)

For the Positive case we'll use (x-3)

Step 3:

Solve the Negative Case

- (x-3) = 12

Multiply

-x+3 = 12

Rearrange and Add up

-x = 9

Multiply both sides by (-1)

x = - 9

Which is the solution for the Negative Case

Step 4:

Solve the Positive Case

(x-3) = 12

Rearrange and Add up

x = 15

Which is the solution for the Positive Case

Step 5:

Wrap up the solution

x=-9

x=15