Solve for a -7=(|a-3|)/-2

$- 7 = \frac{| a - 3 |}{- 2}$

Rewrite the equation as $\frac{| a - 3 |}{- 2} = - 7$ .

$\frac{| a - 3 |}{- 2} = - 7$

Multiply both sides of the equation by $- 2$ .

$- 2 \frac{| a - 3 |}{- 2} = - 2 \cdot - 7$

Simplify both sides of the equation.

Simplify the left side.

Simplify $- 2 \frac{| a - 3 |}{- 2}$ .

Cancel the common factor of $2$ .

Factor $2$ out of $- 2$ .

$2 (- 1) \frac{| a - 3 |}{- 2} = - 2 \cdot - 7$

Factor $2$ out of $- 2$ .

$2 \cdot - 1 \frac{| a - 3 |}{2 \cdot - 1} = - 2 \cdot - 7$

Cancel the common factor.

$2 \cdot - 1 \frac{| a - 3 |}{2 \cdot - 1} = - 2 \cdot - 7$

Rewrite the expression.

$- \frac{| a - 3 |}{- 1} = - 2 \cdot - 7$

Simplify the expression.

Move the negative one from the denominator of $\frac{| a - 3 |}{- 1}$ .

$- (- 1 \cdot | a - 3 |) = - 2 \cdot - 7$

Rewrite $- 1 \cdot | a - 3 |$ as $- | a - 3 |$ .

$- - | a - 3 | = - 2 \cdot - 7$

Multiply $- - | a - 3 |$ .

Multiply $- 1$ by $- 1$ .

$1 | a - 3 | = - 2 \cdot - 7$

Multiply $| a - 3 |$ by $1$ .

$| a - 3 | = - 2 \cdot - 7$

Simplify the right side.

Multiply $- 2$ by $- 7$ .

$| a - 3 | = 14$

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

$a - 3 = \pm 14$

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.

$a - 3 = 14$

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

Add $3$ to both sides of the equation.

$a = 14 + 3$

Add $14$ and $3$ .

$a = 17$

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

$a - 3 = - 14$

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

Add $3$ to both sides of the equation.

$a = - 14 + 3$

Add $- 14$ and $3$ .

$a = - 11$

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

$a = 17, - 11$

Solve for a -7=(|a-3|)/-2

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