Pre-Algebra Examples

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

Step 1

Simplify $\frac{x}{6} + x$ .

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Step 1.1

To write $x$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$\frac{x}{6} + x \cdot \frac{6}{6} = 7$

Step 1.2

Simplify terms.

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Step 1.2.1

Combine $x$ and $\frac{6}{6}$ .

$\frac{x}{6} + \frac{x \cdot 6}{6} = 7$

Step 1.2.2

Combine the numerators over the common denominator.

$\frac{x + x \cdot 6}{6} = 7$

Step 1.3

Simplify the numerator.

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Step 1.3.1

Move $6$ to the left of $x$ .

$\frac{x + 6 \cdot x}{6} = 7$

Step 1.3.2

Add $x$ and $6 x$ .

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

Step 2

Multiply both sides of the equation by $\frac{6}{7}$ .

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

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

Simplify $\frac{6}{7} \cdot \frac{7 x}{6}$ .

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Step 3.1.1.1

Cancel the common factor of $6$ .

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Step 3.1.1.1.1

Cancel the common factor.

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

Step 3.1.1.1.2

Rewrite the expression.

$\frac{1}{7} (7 x) = \frac{6}{7} \cdot 7$

Step 3.1.1.2

Cancel the common factor of $7$ .

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Step 3.1.1.2.1

Factor $7$ out of $7 x$ .

$\frac{1}{7} (7 (x)) = \frac{6}{7} \cdot 7$

Step 3.1.1.2.2

Cancel the common factor.

$\frac{1}{7} (7 x) = \frac{6}{7} \cdot 7$

Step 3.1.1.2.3

Rewrite the expression.

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

Step 3.2

Simplify the right side.

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Step 3.2.1

Cancel the common factor of $7$ .

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Step 3.2.1.1

Cancel the common factor.

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

Step 3.2.1.2

Rewrite the expression.

$x = 6$