Pre-Algebra Examples

$\frac{x}{3} + 4 = 5 + \frac{x}{6}$

Step 1

Move all terms containing $x$ to the left side of the equation.

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Step 1.1

Subtract $\frac{x}{6}$ from both sides of the equation.

$\frac{x}{3} + 4 - \frac{x}{6} = 5$

Step 1.2

To write $\frac{x}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{x}{3} \cdot \frac{2}{2} - \frac{x}{6} + 4 = 5$

Step 1.3

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.3.1

Multiply $\frac{x}{3}$ by $\frac{2}{2}$ .

$\frac{x \cdot 2}{3 \cdot 2} - \frac{x}{6} + 4 = 5$

Step 1.3.2

Multiply $3$ by $2$ .

$\frac{x \cdot 2}{6} - \frac{x}{6} + 4 = 5$

Step 1.4

Combine the numerators over the common denominator.

$\frac{x \cdot 2 - x}{6} + 4 = 5$

Step 1.5

Subtract $x$ from $x \cdot 2$ .

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Step 1.5.1

Reorder $x$ and $2$ .

$\frac{2 \cdot x - x}{6} + 4 = 5$

Step 1.5.2

Subtract $x$ from $2 \cdot x$ .

$\frac{x}{6} + 4 = 5$

Step 2

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

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Step 2.1

Subtract $4$ from both sides of the equation.

$\frac{x}{6} = 5 - 4$

Step 2.2

Subtract $4$ from $5$ .

$\frac{x}{6} = 1$

Step 3

Multiply both sides of the equation by $6$ .

$6 \frac{x}{6} = 6 \cdot 1$

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

Cancel the common factor of $6$ .

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Step 4.1.1.1

Cancel the common factor.

$6 \frac{x}{6} = 6 \cdot 1$

Step 4.1.1.2

Rewrite the expression.

$x = 6 \cdot 1$

Step 4.2

Simplify the right side.

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Step 4.2.1

Multiply $6$ by $1$ .

$x = 6$