Trigonometry Examples

$\frac{| a - 5 |}{8} = 5$

Step 1

Multiply both sides by $8$ .

$\frac{| a - 5 |}{8} \cdot 8 = 5 \cdot 8$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Cancel the common factor of $8$ .

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Step 2.1.1.1

Cancel the common factor.

$\frac{| a - 5 |}{8} \cdot 8 = 5 \cdot 8$

Step 2.1.1.2

Rewrite the expression.

$| a - 5 | = 5 \cdot 8$

Step 2.2

Simplify the right side.

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Step 2.2.1

Multiply $5$ by $8$ .

$| a - 5 | = 40$

Step 3

Solve for $a$ .

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Step 3.1

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

$a - 5 = \pm 40$

Step 3.2

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

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Step 3.2.1

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

$a - 5 = 40$

Step 3.2.2

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

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Step 3.2.2.1

Add $5$ to both sides of the equation.

$a = 40 + 5$

Step 3.2.2.2

Add $40$ and $5$ .

$a = 45$

Step 3.2.3

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

$a - 5 = - 40$

Step 3.2.4

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

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Step 3.2.4.1

Add $5$ to both sides of the equation.

$a = - 40 + 5$

Step 3.2.4.2

Add $- 40$ and $5$ .

$a = - 35$

Step 3.2.5

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

$a = 45, - 35$