Basic Math Examples

$\frac{2}{3} h - 9 = 6 - \frac{2}{3} h$

Step 1

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

$\frac{2 h}{3} - 9 = 6 - \frac{2}{3} h$

Step 2

Simplify each term.

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Step 2.1

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

$\frac{2 h}{3} - 9 = 6 - \frac{h \cdot 2}{3}$

Step 2.2

Move $2$ to the left of $h$ .

$\frac{2 h}{3} - 9 = 6 - \frac{2 h}{3}$

Step 3

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

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Step 3.1

Add $\frac{2 h}{3}$ to both sides of the equation.

$\frac{2 h}{3} - 9 + \frac{2 h}{3} = 6$

Step 3.2

Combine the numerators over the common denominator.

$- 9 + \frac{2 h + 2 h}{3} = 6$

Step 3.3

Add $2 h$ and $2 h$ .

$- 9 + \frac{4 h}{3} = 6$

Step 4

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

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Step 4.1

Add $9$ to both sides of the equation.

$\frac{4 h}{3} = 6 + 9$

Step 4.2

Add $6$ and $9$ .

$\frac{4 h}{3} = 15$

Step 5

Multiply both sides of the equation by $\frac{3}{4}$ .

$\frac{3}{4} \cdot \frac{4 h}{3} = \frac{3}{4} \cdot 15$

Step 6

Simplify both sides of the equation.

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Step 6.1

Simplify the left side.

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Step 6.1.1

Simplify $\frac{3}{4} \cdot \frac{4 h}{3}$ .

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Step 6.1.1.1

Cancel the common factor of $3$ .

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Step 6.1.1.1.1

Cancel the common factor.

$\frac{3}{4} \cdot \frac{4 h}{3} = \frac{3}{4} \cdot 15$

Step 6.1.1.1.2

Rewrite the expression.

$\frac{1}{4} (4 h) = \frac{3}{4} \cdot 15$

Step 6.1.1.2

Cancel the common factor of $4$ .

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Step 6.1.1.2.1

Factor $4$ out of $4 h$ .

$\frac{1}{4} (4 (h)) = \frac{3}{4} \cdot 15$

Step 6.1.1.2.2

Cancel the common factor.

$\frac{1}{4} (4 h) = \frac{3}{4} \cdot 15$

Step 6.1.1.2.3

Rewrite the expression.

$h = \frac{3}{4} \cdot 15$

Step 6.2

Simplify the right side.

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Step 6.2.1

Multiply $\frac{3}{4} \cdot 15$ .

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Step 6.2.1.1

Combine $\frac{3}{4}$ and $15$ .

$h = \frac{3 \cdot 15}{4}$

Step 6.2.1.2

Multiply $3$ by $15$ .

$h = \frac{45}{4}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$h = \frac{45}{4}$

Decimal Form:

$h = 11.25$

Mixed Number Form:

$h = 11 \frac{1}{4}$