Solve for a 39=|-15+4a|

$39 = | - 15 + 4 a |$

Step 1

Rewrite the equation as $| - 15 + 4 a | = 39$ .

$| - 15 + 4 a | = 39$

Step 2

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

$- 15 + 4 a = \pm 39$

Step 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.

$- 15 + 4 a = 39$

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

Add $15$ to both sides of the equation.

$4 a = 39 + 15$

Add $39$ and $15$ .

$4 a = 54$

Divide each term in $4 a = 54$ by $4$ and simplify.

Divide each term in $4 a = 54$ by $4$ .

$\frac{4 a}{4} = \frac{54}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 a}{4} = \frac{54}{4}$

Divide $a$ by $1$ .

$a = \frac{54}{4}$

Simplify the right side.

Cancel the common factor of $54$ and $4$ .

Factor $2$ out of $54$ .

$a = \frac{2 (27)}{4}$

Cancel the common factors.

Factor $2$ out of $4$ .

$a = \frac{2 \cdot 27}{2 \cdot 2}$

Cancel the common factor.

$a = \frac{2 \cdot 27}{2 \cdot 2}$

Rewrite the expression.

$a = \frac{27}{2}$

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

$- 15 + 4 a = - 39$

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

Add $15$ to both sides of the equation.

$4 a = - 39 + 15$

Add $- 39$ and $15$ .

$4 a = - 24$

Divide each term in $4 a = - 24$ by $4$ and simplify.

Divide each term in $4 a = - 24$ by $4$ .

$\frac{4 a}{4} = \frac{- 24}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 a}{4} = \frac{- 24}{4}$

Divide $a$ by $1$ .

$a = \frac{- 24}{4}$

Simplify the right side.

Divide $- 24$ by $4$ .

$a = - 6$

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

$a = \frac{27}{2}, - 6$

Step 4

The result can be shown in multiple forms.

Exact Form:

$a = \frac{27}{2}, - 6$

Decimal Form:

$a = 13.5, - 6$

Mixed Number Form:

$a = 13 \frac{1}{2}, - 6$

Solve for a 39=|-15+4a|

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