Algebra Examples

$\frac{3}{2} h - 2 + \frac{3}{8} h + 4 = \frac{7}{4} h$

Step 1

Simplify $\frac{3}{2} h - 2 + \frac{3}{8} h + 4$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Combine $\frac{3}{2}$ and $h$ .

$\frac{3 h}{2} - 2 + \frac{3}{8} h + 4 = \frac{7}{4} h$

Step 1.1.2

Combine $\frac{3}{8}$ and $h$ .

$\frac{3 h}{2} - 2 + \frac{3 h}{8} + 4 = \frac{7}{4} h$

Step 1.2

To write $\frac{3 h}{2}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{3 h}{2} \cdot \frac{4}{4} + \frac{3 h}{8} - 2 + 4 = \frac{7}{4} h$

Step 1.3

Write each expression with a common denominator of $8$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.3.1

Multiply $\frac{3 h}{2}$ by $\frac{4}{4}$ .

$\frac{3 h \cdot 4}{2 \cdot 4} + \frac{3 h}{8} - 2 + 4 = \frac{7}{4} h$

Step 1.3.2

Multiply $2$ by $4$ .

$\frac{3 h \cdot 4}{8} + \frac{3 h}{8} - 2 + 4 = \frac{7}{4} h$

Step 1.4

Combine the numerators over the common denominator.

$\frac{3 h \cdot 4 + 3 h}{8} - 2 + 4 = \frac{7}{4} h$

Step 1.5

Find the common denominator.

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Step 1.5.1

Write $- 2$ as a fraction with denominator $1$ .

$\frac{3 h \cdot 4 + 3 h}{8} + \frac{- 2}{1} + 4 = \frac{7}{4} h$

Step 1.5.2

Multiply $\frac{- 2}{1}$ by $\frac{8}{8}$ .

$\frac{3 h \cdot 4 + 3 h}{8} + \frac{- 2}{1} \cdot \frac{8}{8} + 4 = \frac{7}{4} h$

Step 1.5.3

Multiply $\frac{- 2}{1}$ by $\frac{8}{8}$ .

$\frac{3 h \cdot 4 + 3 h}{8} + \frac{- 2 \cdot 8}{8} + 4 = \frac{7}{4} h$

Step 1.5.4

Write $4$ as a fraction with denominator $1$ .

$\frac{3 h \cdot 4 + 3 h}{8} + \frac{- 2 \cdot 8}{8} + \frac{4}{1} = \frac{7}{4} h$

Step 1.5.5

Multiply $\frac{4}{1}$ by $\frac{8}{8}$ .

$\frac{3 h \cdot 4 + 3 h}{8} + \frac{- 2 \cdot 8}{8} + \frac{4}{1} \cdot \frac{8}{8} = \frac{7}{4} h$

Step 1.5.6

Multiply $\frac{4}{1}$ by $\frac{8}{8}$ .

$\frac{3 h \cdot 4 + 3 h}{8} + \frac{- 2 \cdot 8}{8} + \frac{4 \cdot 8}{8} = \frac{7}{4} h$

Step 1.6

Combine the numerators over the common denominator.

$\frac{3 h \cdot 4 + 3 h - 2 \cdot 8 + 4 \cdot 8}{8} = \frac{7}{4} h$

Step 1.7

Simplify each term.

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Step 1.7.1

Multiply $4$ by $3$ .

$\frac{12 h + 3 h - 2 \cdot 8 + 4 \cdot 8}{8} = \frac{7}{4} h$

Step 1.7.2

Multiply $- 2$ by $8$ .

$\frac{12 h + 3 h - 16 + 4 \cdot 8}{8} = \frac{7}{4} h$

Step 1.7.3

Multiply $4$ by $8$ .

$\frac{12 h + 3 h - 16 + 32}{8} = \frac{7}{4} h$

Step 1.8

Simplify by adding terms.

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Step 1.8.1

Add $12 h$ and $3 h$ .

$\frac{15 h - 16 + 32}{8} = \frac{7}{4} h$

Step 1.8.2

Add $- 16$ and $32$ .

$\frac{15 h + 16}{8} = \frac{7}{4} h$

Step 2

Combine $\frac{7}{4}$ and $h$ .

$\frac{15 h + 16}{8} = \frac{7 h}{4}$

Step 3

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

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Step 3.1

Subtract $\frac{7 h}{4}$ from both sides of the equation.

$\frac{15 h + 16}{8} - \frac{7 h}{4} = 0$

Step 3.2

To write $- \frac{7 h}{4}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{15 h + 16}{8} - \frac{7 h}{4} \cdot \frac{2}{2} = 0$

Step 3.3

Write each expression with a common denominator of $8$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.3.1

Multiply $\frac{7 h}{4}$ by $\frac{2}{2}$ .

$\frac{15 h + 16}{8} - \frac{7 h \cdot 2}{4 \cdot 2} = 0$

Step 3.3.2

Multiply $4$ by $2$ .

$\frac{15 h + 16}{8} - \frac{7 h \cdot 2}{8} = 0$

Step 3.4

Combine the numerators over the common denominator.

$\frac{15 h + 16 - 7 h \cdot 2}{8} = 0$

Step 3.5

Simplify the numerator.

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Step 3.5.1

Multiply $2$ by $- 7$ .

$\frac{15 h + 16 - 14 h}{8} = 0$

Step 3.5.2

Subtract $14 h$ from $15 h$ .

$\frac{h + 16}{8} = 0$

Step 4

Set the numerator equal to zero.

$h + 16 = 0$

Step 5

Subtract $16$ from both sides of the equation.

$h = - 16$