Question

Solve for the equation, show all your work. This is an absolute value equation. You need to show both equations and the work for both. Don't forget to check your answers.
|3x - 9| = 12

Answer 1

Answer:

$x=-1$ or $7$

Step-by-step explanation:

We use casework on when $3x-9=12$ and when $3x-9=-12$.

For the first case, $3x-9=12$, we add 9 to both sides to get

$3x=21$.

Dividing both sides by 3 gives

$x=7.$

For the second case, $3x-9=-12$, we add 9 to both sides to get

$3x=-3$.

Dividing both sides by 3 gives

$x=-1$.

Checking both cases, we plug in $x=7$ and $x=-1$.

For the first case, we have $|3(7)-9|=|21-9|=|12|=12$,  which satisfies the equation.

For the second case, we have $|3(-1)-9|=|-3-9|=|-12|=12$, which also satisfies the equation.

This gives us two solutions to the equation; $x=7$ and $x=-1$.