Solve for q |4q+12|=4

$| 4 q + 12 | = 4$

Step 1

Remove the absolute value term. This creates a $\pm$ on the right side of the equation because $| x | = \pm x$ .

$4 q + 12 = \pm 4$

Step 2

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$4 q + 12 = 4$

Move all terms not containing $q$ to the right side of the equation.

Subtract $12$ from both sides of the equation.

$4 q = 4 - 12$

Subtract $12$ from $4$ .

$4 q = - 8$

Divide each term in $4 q = - 8$ by $4$ and simplify.

Divide each term in $4 q = - 8$ by $4$ .

$\frac{4 q}{4} = \frac{- 8}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 q}{4} = \frac{- 8}{4}$

Divide $q$ by $1$ .

$q = \frac{- 8}{4}$

Simplify the right side.

Divide $- 8$ by $4$ .

$q = - 2$

Next, use the negative value of the $\pm$ to find the second solution.

$4 q + 12 = - 4$

Move all terms not containing $q$ to the right side of the equation.

Subtract $12$ from both sides of the equation.

$4 q = - 4 - 12$

Subtract $12$ from $- 4$ .

$4 q = - 16$

Divide each term in $4 q = - 16$ by $4$ and simplify.

Divide each term in $4 q = - 16$ by $4$ .

$\frac{4 q}{4} = \frac{- 16}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 q}{4} = \frac{- 16}{4}$

Divide $q$ by $1$ .

$q = \frac{- 16}{4}$

Simplify the right side.

Divide $- 16$ by $4$ .

$q = - 4$

The complete solution is the result of both the positive and negative portions of the solution.

$q = - 2, - 4$

Solve for q |4q+12|=4

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