Finite Math Examples

$\frac{3 h}{4} - \frac{1}{2} = \frac{5 h}{8}$

Step 1

Multiply both sides by $8$ .

$(\frac{3 h}{4} - \frac{1}{2}) \cdot 8 = \frac{5 h}{8} \cdot 8$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $(\frac{3 h}{4} - \frac{1}{2}) \cdot 8$ .

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Step 2.1.1.1

Apply the distributive property.

$\frac{3 h}{4} \cdot 8 - \frac{1}{2} \cdot 8 = \frac{5 h}{8} \cdot 8$

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 $8$ .

$\frac{3 h}{4} \cdot (4 (2)) - \frac{1}{2} \cdot 8 = \frac{5 h}{8} \cdot 8$

Step 2.1.1.2.2

Cancel the common factor.

$\frac{3 h}{4} \cdot (4 \cdot 2) - \frac{1}{2} \cdot 8 = \frac{5 h}{8} \cdot 8$

Step 2.1.1.2.3

Rewrite the expression.

$3 h \cdot 2 - \frac{1}{2} \cdot 8 = \frac{5 h}{8} \cdot 8$

Step 2.1.1.3

Multiply $2$ by $3$ .

$6 h - \frac{1}{2} \cdot 8 = \frac{5 h}{8} \cdot 8$

Step 2.1.1.4

Cancel the common factor of $2$ .

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Step 2.1.1.4.1

Move the leading negative in $- \frac{1}{2}$ into the numerator.

$6 h + \frac{- 1}{2} \cdot 8 = \frac{5 h}{8} \cdot 8$

Step 2.1.1.4.2

Factor $2$ out of $8$ .

$6 h + \frac{- 1}{2} \cdot (2 (4)) = \frac{5 h}{8} \cdot 8$

Step 2.1.1.4.3

Cancel the common factor.

$6 h + \frac{- 1}{2} \cdot (2 \cdot 4) = \frac{5 h}{8} \cdot 8$

Step 2.1.1.4.4

Rewrite the expression.

$6 h - 1 \cdot 4 = \frac{5 h}{8} \cdot 8$

Step 2.1.1.5

Multiply $- 1$ by $4$ .

$6 h - 4 = \frac{5 h}{8} \cdot 8$

Step 2.2

Simplify the right side.

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Step 2.2.1

Cancel the common factor of $8$ .

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Step 2.2.1.1

Cancel the common factor.

$6 h - 4 = \frac{5 h}{8} \cdot 8$

Step 2.2.1.2

Rewrite the expression.

$6 h - 4 = 5 h$

Step 3

Solve for $h$ .

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Step 3.1

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

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Step 3.1.1

Subtract $5 h$ from both sides of the equation.

$6 h - 4 - 5 h = 0$

Step 3.1.2

Subtract $5 h$ from $6 h$ .

$h - 4 = 0$

Step 3.2

Add $4$ to both sides of the equation.

$h = 4$