Algebra Examples

$\frac{5 u}{8} + 2 = \frac{7 u}{12}$

Step 1

Multiply both sides by $12$ .

$(\frac{5 u}{8} + 2) \cdot 12 = \frac{7 u}{12} \cdot 12$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $(\frac{5 u}{8} + 2) \cdot 12$ .

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Step 2.1.1.1

Apply the distributive property.

$\frac{5 u}{8} \cdot 12 + 2 \cdot 12 = \frac{7 u}{12} \cdot 12$

Step 2.1.1.2

Cancel the common factor of $4$ .

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Step 2.1.1.2.1

Factor $4$ out of $8$ .

$\frac{5 u}{4 (2)} \cdot 12 + 2 \cdot 12 = \frac{7 u}{12} \cdot 12$

Step 2.1.1.2.2

Factor $4$ out of $12$ .

$\frac{5 u}{4 \cdot 2} \cdot (4 \cdot 3) + 2 \cdot 12 = \frac{7 u}{12} \cdot 12$

Step 2.1.1.2.3

Cancel the common factor.

$\frac{5 u}{4 \cdot 2} \cdot (4 \cdot 3) + 2 \cdot 12 = \frac{7 u}{12} \cdot 12$

Step 2.1.1.2.4

Rewrite the expression.

$\frac{5 u}{2} \cdot 3 + 2 \cdot 12 = \frac{7 u}{12} \cdot 12$

Step 2.1.1.3

Combine $\frac{5 u}{2}$ and $3$ .

$\frac{5 u \cdot 3}{2} + 2 \cdot 12 = \frac{7 u}{12} \cdot 12$

Step 2.1.1.4

Multiply.

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Step 2.1.1.4.1

Multiply $3$ by $5$ .

$\frac{15 u}{2} + 2 \cdot 12 = \frac{7 u}{12} \cdot 12$

Step 2.1.1.4.2

Multiply $2$ by $12$ .

$\frac{15 u}{2} + 24 = \frac{7 u}{12} \cdot 12$

Step 2.2

Simplify the right side.

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Step 2.2.1

Cancel the common factor of $12$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{15 u}{2} + 24 = \frac{7 u}{12} \cdot 12$

Step 2.2.1.2

Rewrite the expression.

$\frac{15 u}{2} + 24 = 7 u$

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 $7 u$ from both sides of the equation.

$\frac{15 u}{2} + 24 - 7 u = 0$

Step 3.1.2

To write $- 7 u$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{15 u}{2} - 7 u \cdot \frac{2}{2} + 24 = 0$

Step 3.1.3

Combine $- 7 u$ and $\frac{2}{2}$ .

$\frac{15 u}{2} + \frac{- 7 u \cdot 2}{2} + 24 = 0$

Step 3.1.4

Combine the numerators over the common denominator.

$\frac{15 u - 7 u \cdot 2}{2} + 24 = 0$

Step 3.1.5

Simplify each term.

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Step 3.1.5.1

Simplify the numerator.

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Step 3.1.5.1.1

Factor $u$ out of $15 u - 7 u \cdot 2$ .

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Step 3.1.5.1.1.1

Factor $u$ out of $15 u$ .

$\frac{u \cdot 15 - 7 u \cdot 2}{2} + 24 = 0$

Step 3.1.5.1.1.2

Factor $u$ out of $- 7 u \cdot 2$ .

$\frac{u \cdot 15 + u (- 7 \cdot 2)}{2} + 24 = 0$

Step 3.1.5.1.1.3

Factor $u$ out of $u \cdot 15 + u (- 7 \cdot 2)$ .

$\frac{u (15 - 7 \cdot 2)}{2} + 24 = 0$

Step 3.1.5.1.2

Multiply $- 7$ by $2$ .

$\frac{u (15 - 14)}{2} + 24 = 0$

Step 3.1.5.1.3

Subtract $14$ from $15$ .

$\frac{u \cdot 1}{2} + 24 = 0$

Step 3.1.5.2

Multiply $u$ by $1$ .

$\frac{u}{2} + 24 = 0$

Step 3.2

Subtract $24$ from both sides of the equation.

$\frac{u}{2} = - 24$

Step 3.3

Multiply both sides of the equation by $2$ .

$2 \frac{u}{2} = 2 \cdot - 24$

Step 3.4

Simplify both sides of the equation.

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Step 3.4.1

Simplify the left side.

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Step 3.4.1.1

Cancel the common factor of $2$ .

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Step 3.4.1.1.1

Cancel the common factor.

$2 \frac{u}{2} = 2 \cdot - 24$

Step 3.4.1.1.2

Rewrite the expression.

$u = 2 \cdot - 24$

Step 3.4.2

Simplify the right side.

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Step 3.4.2.1

Multiply $2$ by $- 24$ .

$u = - 48$