Algebra Examples

$- \frac{7}{9} m = \frac{11}{6}$

Step 1

Multiply both sides of the equation by $- \frac{9}{7}$ .

$- \frac{9}{7} (- \frac{7}{9} m) = - \frac{9}{7} \cdot \frac{11}{6}$

Step 2

Simplify both sides of the equation.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $- \frac{9}{7} (- \frac{7}{9} m)$ .

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Step 2.1.1.1

Combine $m$ and $\frac{7}{9}$ .

$- \frac{9}{7} (- \frac{m \cdot 7}{9}) = - \frac{9}{7} \cdot \frac{11}{6}$

Step 2.1.1.2

Cancel the common factor of $9$ .

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Step 2.1.1.2.1

Move the leading negative in $- \frac{9}{7}$ into the numerator.

$\frac{- 9}{7} (- \frac{m \cdot 7}{9}) = - \frac{9}{7} \cdot \frac{11}{6}$

Step 2.1.1.2.2

Move the leading negative in $- \frac{m \cdot 7}{9}$ into the numerator.

$\frac{- 9}{7} \cdot \frac{- m \cdot 7}{9} = - \frac{9}{7} \cdot \frac{11}{6}$

Step 2.1.1.2.3

Factor $9$ out of $- 9$ .

$\frac{9 (- 1)}{7} \cdot \frac{- m \cdot 7}{9} = - \frac{9}{7} \cdot \frac{11}{6}$

Step 2.1.1.2.4

Cancel the common factor.

$\frac{9 \cdot - 1}{7} \cdot \frac{- m \cdot 7}{9} = - \frac{9}{7} \cdot \frac{11}{6}$

Step 2.1.1.2.5

Rewrite the expression.

$\frac{- 1}{7} (- m \cdot 7) = - \frac{9}{7} \cdot \frac{11}{6}$

Step 2.1.1.3

Cancel the common factor of $7$ .

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Step 2.1.1.3.1

Factor $7$ out of $- m \cdot 7$ .

$\frac{- 1}{7} (7 \cdot (- m)) = - \frac{9}{7} \cdot \frac{11}{6}$

Step 2.1.1.3.2

Cancel the common factor.

$\frac{- 1}{7} (7 \cdot (- m)) = - \frac{9}{7} \cdot \frac{11}{6}$

Step 2.1.1.3.3

Rewrite the expression.

$- - m = - \frac{9}{7} \cdot \frac{11}{6}$

Step 2.1.1.4

Multiply.

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Step 2.1.1.4.1

Multiply $- 1$ by $- 1$ .

$1 m = - \frac{9}{7} \cdot \frac{11}{6}$

Step 2.1.1.4.2

Multiply $m$ by $1$ .

$m = - \frac{9}{7} \cdot \frac{11}{6}$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $- \frac{9}{7} \cdot \frac{11}{6}$ .

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Step 2.2.1.1

Cancel the common factor of $3$ .

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Step 2.2.1.1.1

Move the leading negative in $- \frac{9}{7}$ into the numerator.

$m = \frac{- 9}{7} \cdot \frac{11}{6}$

Step 2.2.1.1.2

Factor $3$ out of $- 9$ .

$m = \frac{3 (- 3)}{7} \cdot \frac{11}{6}$

Step 2.2.1.1.3

Factor $3$ out of $6$ .

$m = \frac{3 \cdot - 3}{7} \cdot \frac{11}{3 \cdot 2}$

Step 2.2.1.1.4

Cancel the common factor.

$m = \frac{3 \cdot - 3}{7} \cdot \frac{11}{3 \cdot 2}$

Step 2.2.1.1.5

Rewrite the expression.

$m = \frac{- 3}{7} \cdot \frac{11}{2}$

Step 2.2.1.2

Multiply $\frac{- 3}{7}$ by $\frac{11}{2}$ .

$m = \frac{- 3 \cdot 11}{7 \cdot 2}$

Step 2.2.1.3

Simplify the expression.

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Step 2.2.1.3.1

Multiply $- 3$ by $11$ .

$m = \frac{- 33}{7 \cdot 2}$

Step 2.2.1.3.2

Multiply $7$ by $2$ .

$m = \frac{- 33}{14}$

Step 2.2.1.3.3

Move the negative in front of the fraction.

$m = - \frac{33}{14}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$m = - \frac{33}{14}$

Decimal Form:

$m = - 2.35714285 \dots$

Mixed Number Form:

$m = - 2 \frac{5}{14}$