Algebra Examples

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

Step 1

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

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

Step 2

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

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

Step 3

Simplify both sides of the equation.

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Step 3.1

Simplify the left side.

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Step 3.1.1

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

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Step 3.1.1.1

Cancel the common factor of $2$ .

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Step 3.1.1.1.1

Factor $2$ out of $- 2$ .

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

Step 3.1.1.1.2

Factor $2$ out of $- 2$ .

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

Step 3.1.1.1.3

Cancel the common factor.

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

Step 3.1.1.1.4

Rewrite the expression.

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

Step 3.1.1.2

Simplify the expression.

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Step 3.1.1.2.1

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

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

Step 3.1.1.2.2

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

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

Step 3.1.1.3

Multiply $- - | a - 3 |$ .

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Step 3.1.1.3.1

Multiply $- 1$ by $- 1$ .

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

Step 3.1.1.3.2

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

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

Step 3.2

Simplify the right side.

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Step 3.2.1

Multiply $- 2$ by $- 7$ .

$| a - 3 | = 14$

Step 4

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

$a - 3 = \pm 14$

Step 5

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

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Step 5.1

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

$a - 3 = 14$

Step 5.2

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

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Step 5.2.1

Add $3$ to both sides of the equation.

$a = 14 + 3$

Step 5.2.2

Add $14$ and $3$ .

$a = 17$

Step 5.3

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

$a - 3 = - 14$

Step 5.4

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

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Step 5.4.1

Add $3$ to both sides of the equation.

$a = - 14 + 3$

Step 5.4.2

Add $- 14$ and $3$ .

$a = - 11$

Step 5.5

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

$a = 17, - 11$