Pre-Algebra Examples

$\frac{7}{9} x - 5 = 5$

Step 1

Combine $\frac{7}{9}$ and $x$ .

$\frac{7 x}{9} - 5 = 5$

Step 2

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

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Step 2.1

Add $5$ to both sides of the equation.

$\frac{7 x}{9} = 5 + 5$

Step 2.2

Add $5$ and $5$ .

$\frac{7 x}{9} = 10$

Step 3

Multiply both sides of the equation by $\frac{9}{7}$ .

$\frac{9}{7} \cdot \frac{7 x}{9} = \frac{9}{7} \cdot 10$

Step 4

Simplify both sides of the equation.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Simplify $\frac{9}{7} \cdot \frac{7 x}{9}$ .

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Step 4.1.1.1

Cancel the common factor of $9$ .

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Step 4.1.1.1.1

Cancel the common factor.

$\frac{9}{7} \cdot \frac{7 x}{9} = \frac{9}{7} \cdot 10$

Step 4.1.1.1.2

Rewrite the expression.

$\frac{1}{7} (7 x) = \frac{9}{7} \cdot 10$

Step 4.1.1.2

Cancel the common factor of $7$ .

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Step 4.1.1.2.1

Factor $7$ out of $7 x$ .

$\frac{1}{7} (7 (x)) = \frac{9}{7} \cdot 10$

Step 4.1.1.2.2

Cancel the common factor.

$\frac{1}{7} (7 x) = \frac{9}{7} \cdot 10$

Step 4.1.1.2.3

Rewrite the expression.

$x = \frac{9}{7} \cdot 10$

Step 4.2

Simplify the right side.

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Step 4.2.1

Multiply $\frac{9}{7} \cdot 10$ .

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Step 4.2.1.1

Combine $\frac{9}{7}$ and $10$ .

$x = \frac{9 \cdot 10}{7}$

Step 4.2.1.2

Multiply $9$ by $10$ .

$x = \frac{90}{7}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{90}{7}$

Decimal Form:

$x = 12.85714285 \dots$

Mixed Number Form:

$x = 12 \frac{6}{7}$