Basic Math Examples

$| \frac{a + 6}{7} | = 9$

Step 1

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

$\frac{a + 6}{7} = \pm 9$

Step 2

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

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Step 2.1

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

$\frac{a + 6}{7} = 9$

Step 2.2

Multiply both sides of the equation by $7$ .

$7 \frac{a + 6}{7} = 7 \cdot 9$

Step 2.3

Simplify both sides of the equation.

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Step 2.3.1

Simplify the left side.

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Step 2.3.1.1

Cancel the common factor of $7$ .

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Step 2.3.1.1.1

Cancel the common factor.

$7 \frac{a + 6}{7} = 7 \cdot 9$

Step 2.3.1.1.2

Rewrite the expression.

$a + 6 = 7 \cdot 9$

Step 2.3.2

Simplify the right side.

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Step 2.3.2.1

Multiply $7$ by $9$ .

$a + 6 = 63$

Step 2.4

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

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Step 2.4.1

Subtract $6$ from both sides of the equation.

$a = 63 - 6$

Step 2.4.2

Subtract $6$ from $63$ .

$a = 57$

Step 2.5

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

$\frac{a + 6}{7} = - 9$

Step 2.6

Multiply both sides of the equation by $7$ .

$7 \frac{a + 6}{7} = 7 \cdot - 9$

Step 2.7

Simplify both sides of the equation.

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Step 2.7.1

Simplify the left side.

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Step 2.7.1.1

Cancel the common factor of $7$ .

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Step 2.7.1.1.1

Cancel the common factor.

$7 \frac{a + 6}{7} = 7 \cdot - 9$

Step 2.7.1.1.2

Rewrite the expression.

$a + 6 = 7 \cdot - 9$

Step 2.7.2

Simplify the right side.

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Step 2.7.2.1

Multiply $7$ by $- 9$ .

$a + 6 = - 63$

Step 2.8

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

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Step 2.8.1

Subtract $6$ from both sides of the equation.

$a = - 63 - 6$

Step 2.8.2

Subtract $6$ from $- 63$ .

$a = - 69$

Step 2.9

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

$a = 57, - 69$