Solve for a |6+3a|=15

$| 6 + 3 a | = 15$

Step 1

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

$6 + 3 a = \pm 15$

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.

$6 + 3 a = 15$

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

Subtract $6$ from both sides of the equation.

$3 a = 15 - 6$

Subtract $6$ from $15$ .

$3 a = 9$

Divide each term in $3 a = 9$ by $3$ and simplify.

Divide each term in $3 a = 9$ by $3$ .

$\frac{3 a}{3} = \frac{9}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 a}{3} = \frac{9}{3}$

Divide $a$ by $1$ .

$a = \frac{9}{3}$

Simplify the right side.

Divide $9$ by $3$ .

$a = 3$

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

$6 + 3 a = - 15$

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

Subtract $6$ from both sides of the equation.

$3 a = - 15 - 6$

Subtract $6$ from $- 15$ .

$3 a = - 21$

Divide each term in $3 a = - 21$ by $3$ and simplify.

Divide each term in $3 a = - 21$ by $3$ .

$\frac{3 a}{3} = \frac{- 21}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 a}{3} = \frac{- 21}{3}$

Divide $a$ by $1$ .

$a = \frac{- 21}{3}$

Simplify the right side.

Divide $- 21$ by $3$ .

$a = - 7$

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

$a = 3, - 7$

Solve for a |6+3a|=15

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