Solve the Absolute Value Inequality for a -5|6a+21|=-15

$- 5 | 6 a + 21 | = - 15$

Divide each term in $- 5 | 6 a + 21 | = - 15$ by $- 5$ and simplify.

Divide each term in $- 5 | 6 a + 21 | = - 15$ by $- 5$ .

$\frac{- 5 | 6 a + 21 |}{- 5} = \frac{- 15}{- 5}$

Simplify the left side.

Cancel the common factor of $- 5$ .

Cancel the common factor.

$\frac{- 5 | 6 a + 21 |}{- 5} = \frac{- 15}{- 5}$

Divide $| 6 a + 21 |$ by $1$ .

$| 6 a + 21 | = \frac{- 15}{- 5}$

Simplify the right side.

Divide $- 15$ by $- 5$ .

$| 6 a + 21 | = 3$

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

$6 a + 21 = \pm 3$

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.

$6 a + 21 = 3$

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

Subtract $21$ from both sides of the equation.

$6 a = 3 - 21$

Subtract $21$ from $3$ .

$6 a = - 18$

Divide each term in $6 a = - 18$ by $6$ and simplify.

Divide each term in $6 a = - 18$ by $6$ .

$\frac{6 a}{6} = \frac{- 18}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 a}{6} = \frac{- 18}{6}$

Divide $a$ by $1$ .

$a = \frac{- 18}{6}$

Simplify the right side.

Divide $- 18$ by $6$ .

$a = - 3$

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

$6 a + 21 = - 3$

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

Subtract $21$ from both sides of the equation.

$6 a = - 3 - 21$

Subtract $21$ from $- 3$ .

$6 a = - 24$

Divide each term in $6 a = - 24$ by $6$ and simplify.

Divide each term in $6 a = - 24$ by $6$ .

$\frac{6 a}{6} = \frac{- 24}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 a}{6} = \frac{- 24}{6}$

Divide $a$ by $1$ .

$a = \frac{- 24}{6}$

Simplify the right side.

Divide $- 24$ by $6$ .

$a = - 4$

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

$a = - 3, - 4$

Solve the Absolute Value Inequality for a -5|6a+21|=-15

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