Basic Math Examples

$\frac{6}{7} h + 13 = - 9$

Step 1

Combine $\frac{6}{7}$ and $h$ .

$\frac{6 h}{7} + 13 = - 9$

Step 2

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

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Step 2.1

Subtract $13$ from both sides of the equation.

$\frac{6 h}{7} = - 9 - 13$

Step 2.2

Subtract $13$ from $- 9$ .

$\frac{6 h}{7} = - 22$

Step 3

Multiply both sides of the equation by $\frac{7}{6}$ .

$\frac{7}{6} \cdot \frac{6 h}{7} = \frac{7}{6} \cdot - 22$

Step 4

Simplify both sides of the equation.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Simplify $\frac{7}{6} \cdot \frac{6 h}{7}$ .

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Step 4.1.1.1

Cancel the common factor of $7$ .

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Step 4.1.1.1.1

Cancel the common factor.

$\frac{7}{6} \cdot \frac{6 h}{7} = \frac{7}{6} \cdot - 22$

Step 4.1.1.1.2

Rewrite the expression.

$\frac{1}{6} (6 h) = \frac{7}{6} \cdot - 22$

Step 4.1.1.2

Cancel the common factor of $6$ .

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Step 4.1.1.2.1

Factor $6$ out of $6 h$ .

$\frac{1}{6} (6 (h)) = \frac{7}{6} \cdot - 22$

Step 4.1.1.2.2

Cancel the common factor.

$\frac{1}{6} (6 h) = \frac{7}{6} \cdot - 22$

Step 4.1.1.2.3

Rewrite the expression.

$h = \frac{7}{6} \cdot - 22$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $\frac{7}{6} \cdot - 22$ .

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Step 4.2.1.1

Cancel the common factor of $2$ .

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Step 4.2.1.1.1

Factor $2$ out of $6$ .

$h = \frac{7}{2 (3)} \cdot - 22$

Step 4.2.1.1.2

Factor $2$ out of $- 22$ .

$h = \frac{7}{2 \cdot 3} \cdot (2 \cdot - 11)$

Step 4.2.1.1.3

Cancel the common factor.

$h = \frac{7}{2 \cdot 3} \cdot (2 \cdot - 11)$

Step 4.2.1.1.4

Rewrite the expression.

$h = \frac{7}{3} \cdot - 11$

Step 4.2.1.2

Combine $\frac{7}{3}$ and $- 11$ .

$h = \frac{7 \cdot - 11}{3}$

Step 4.2.1.3

Simplify the expression.

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Step 4.2.1.3.1

Multiply $7$ by $- 11$ .

$h = \frac{- 77}{3}$

Step 4.2.1.3.2

Move the negative in front of the fraction.

$h = - \frac{77}{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$h = - \frac{77}{3}$

Decimal Form:

$h = - 25.\overline{6}$

Mixed Number Form:

$h = - 25 \frac{2}{3}$