Algebra Examples

$\frac{x - 2}{5} + 8 = 11$

Step 1

Simplify $\frac{x - 2}{5} + 8$ .

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Step 1.1

To write $8$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{x - 2}{5} + 8 \cdot \frac{5}{5} = 11$

Step 1.2

Simplify terms.

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Step 1.2.1

Combine $8$ and $\frac{5}{5}$ .

$\frac{x - 2}{5} + \frac{8 \cdot 5}{5} = 11$

Step 1.2.2

Combine the numerators over the common denominator.

$\frac{x - 2 + 8 \cdot 5}{5} = 11$

Step 1.3

Simplify the numerator.

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Step 1.3.1

Multiply $8$ by $5$ .

$\frac{x - 2 + 40}{5} = 11$

Step 1.3.2

Add $- 2$ and $40$ .

$\frac{x + 38}{5} = 11$

Step 2

Multiply both sides of the equation by $5$ .

$5 \frac{x + 38}{5} = 5 \cdot 11$

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

Cancel the common factor of $5$ .

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Step 3.1.1.1

Cancel the common factor.

$5 \frac{x + 38}{5} = 5 \cdot 11$

Step 3.1.1.2

Rewrite the expression.

$x + 38 = 5 \cdot 11$

Step 3.2

Simplify the right side.

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Step 3.2.1

Multiply $5$ by $11$ .

$x + 38 = 55$

Step 4

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

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Step 4.1

Subtract $38$ from both sides of the equation.

$x = 55 - 38$

Step 4.2

Subtract $38$ from $55$ .

$x = 17$