Pre-Algebra Examples

$\frac{u}{3} = \frac{u}{5} + 4$

Step 1

Multiply both sides by $3$ .

$\frac{u}{3} \cdot 3 = (\frac{u}{5} + 4) \cdot 3$

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 $3$ .

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Step 2.1.1.1

Cancel the common factor.

$\frac{u}{3} \cdot 3 = (\frac{u}{5} + 4) \cdot 3$

Step 2.1.1.2

Rewrite the expression.

$u = (\frac{u}{5} + 4) \cdot 3$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $(\frac{u}{5} + 4) \cdot 3$ .

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Step 2.2.1.1

Simplify terms.

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Step 2.2.1.1.1

Apply the distributive property.

$u = \frac{u}{5} \cdot 3 + 4 \cdot 3$

Step 2.2.1.1.2

Combine $\frac{u}{5}$ and $3$ .

$u = \frac{u \cdot 3}{5} + 4 \cdot 3$

Step 2.2.1.1.3

Multiply $4$ by $3$ .

$u = \frac{u \cdot 3}{5} + 12$

Step 2.2.1.2

Move $3$ to the left of $u$ .

$u = \frac{3 u}{5} + 12$

Step 3

Solve for $u$ .

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Step 3.1

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

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Step 3.1.1

Subtract $\frac{3 u}{5}$ from both sides of the equation.

$u - \frac{3 u}{5} = 12$

Step 3.1.2

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

$u \cdot \frac{5}{5} - \frac{3 u}{5} = 12$

Step 3.1.3

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

$\frac{u \cdot 5}{5} - \frac{3 u}{5} = 12$

Step 3.1.4

Combine the numerators over the common denominator.

$\frac{u \cdot 5 - 3 u}{5} = 12$

Step 3.1.5

Simplify the numerator.

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Step 3.1.5.1

Move $5$ to the left of $u$ .

$\frac{5 \cdot u - 3 u}{5} = 12$

Step 3.1.5.2

Subtract $3 u$ from $5 u$ .

$\frac{2 u}{5} = 12$

Step 3.2

Multiply both sides of the equation by $\frac{5}{2}$ .

$\frac{5}{2} \cdot \frac{2 u}{5} = \frac{5}{2} \cdot 12$

Step 3.3

Simplify both sides of the equation.

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Step 3.3.1

Simplify the left side.

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Step 3.3.1.1

Simplify $\frac{5}{2} \cdot \frac{2 u}{5}$ .

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Step 3.3.1.1.1

Cancel the common factor of $5$ .

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Step 3.3.1.1.1.1

Cancel the common factor.

$\frac{5}{2} \cdot \frac{2 u}{5} = \frac{5}{2} \cdot 12$

Step 3.3.1.1.1.2

Rewrite the expression.

$\frac{1}{2} (2 u) = \frac{5}{2} \cdot 12$

Step 3.3.1.1.2

Cancel the common factor of $2$ .

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Step 3.3.1.1.2.1

Factor $2$ out of $2 u$ .

$\frac{1}{2} (2 (u)) = \frac{5}{2} \cdot 12$

Step 3.3.1.1.2.2

Cancel the common factor.

$\frac{1}{2} (2 u) = \frac{5}{2} \cdot 12$

Step 3.3.1.1.2.3

Rewrite the expression.

$u = \frac{5}{2} \cdot 12$

Step 3.3.2

Simplify the right side.

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Step 3.3.2.1

Simplify $\frac{5}{2} \cdot 12$ .

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Step 3.3.2.1.1

Cancel the common factor of $2$ .

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Step 3.3.2.1.1.1

Factor $2$ out of $12$ .

$u = \frac{5}{2} \cdot (2 (6))$

Step 3.3.2.1.1.2

Cancel the common factor.

$u = \frac{5}{2} \cdot (2 \cdot 6)$

Step 3.3.2.1.1.3

Rewrite the expression.

$u = 5 \cdot 6$

Step 3.3.2.1.2

Multiply $5$ by $6$ .

$u = 30$