Solve for a |(a+6)/7|=9

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

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

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

Set up the positive portion of the $\pm$ solution.

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

Solve the first equation for $a$ .

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Multiply both sides of the equation by $7$ .

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

Simplify both sides of the equation.

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Cancel the common factor of $7$ .

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Cancel the common factor.

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

Rewrite the expression.

$a + 6 = 7 \cdot 9$

Multiply $7$ by $9$ .

$a + 6 = 63$

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

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Subtract $6$ from both sides of the equation.

$a = 63 - 6$

Subtract $6$ from $63$ .

$a = 57$

Set up the negative portion of the $\pm$ solution.

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

Solve the second equation for $a$ .

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Multiply both sides of the equation by $7$ .

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

Simplify both sides of the equation.

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Cancel the common factor of $7$ .

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Cancel the common factor.

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

Rewrite the expression.

$a + 6 = 7 \cdot (- 9)$

Multiply $7$ by $- 9$ .

$a + 6 = - 63$

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

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Subtract $6$ from both sides of the equation.

$a = - 63 - 6$

Subtract $6$ from $- 63$ .

$a = - 69$

The solution to the equation includes both the positive and negative portions of the solution.

$a = 57, - 69$

Solve for a |(a+6)/7|=9

Solving MATH problems