Algebra Examples

$\frac{2 m}{5} = \frac{1}{3} (2 m - 12)$

Step 1

Multiply both sides by $5$ .

$\frac{2 m}{5} \cdot 5 = \frac{1}{3} \cdot (2 m - 12) \cdot 5$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Cancel the common factor of $5$ .

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Step 2.1.1.1

Cancel the common factor.

$\frac{2 m}{5} \cdot 5 = \frac{1}{3} \cdot (2 m - 12) \cdot 5$

Step 2.1.1.2

Rewrite the expression.

$2 m = \frac{1}{3} \cdot (2 m - 12) \cdot 5$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $\frac{1}{3} \cdot (2 m - 12) \cdot 5$ .

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Step 2.2.1.1

Apply the distributive property.

$2 m = (\frac{1}{3} (2 m) + \frac{1}{3} \cdot - 12) \cdot 5$

Step 2.2.1.2

Multiply $\frac{1}{3} (2 m)$ .

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Step 2.2.1.2.1

Combine $2$ and $\frac{1}{3}$ .

$2 m = (\frac{2}{3} m + \frac{1}{3} \cdot - 12) \cdot 5$

Step 2.2.1.2.2

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

$2 m = (\frac{2 m}{3} + \frac{1}{3} \cdot - 12) \cdot 5$

Step 2.2.1.3

Cancel the common factor of $3$ .

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Step 2.2.1.3.1

Factor $3$ out of $- 12$ .

$2 m = (\frac{2 m}{3} + \frac{1}{3} \cdot (3 (- 4))) \cdot 5$

Step 2.2.1.3.2

Cancel the common factor.

$2 m = (\frac{2 m}{3} + \frac{1}{3} \cdot (3 \cdot - 4)) \cdot 5$

Step 2.2.1.3.3

Rewrite the expression.

$2 m = (\frac{2 m}{3} - 4) \cdot 5$

Step 2.2.1.4

Apply the distributive property.

$2 m = \frac{2 m}{3} \cdot 5 - 4 \cdot 5$

Step 2.2.1.5

Multiply $\frac{2 m}{3} \cdot 5$ .

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Step 2.2.1.5.1

Combine $\frac{2 m}{3}$ and $5$ .

$2 m = \frac{2 m \cdot 5}{3} - 4 \cdot 5$

Step 2.2.1.5.2

Multiply $5$ by $2$ .

$2 m = \frac{10 m}{3} - 4 \cdot 5$

Step 2.2.1.6

Multiply $- 4$ by $5$ .

$2 m = \frac{10 m}{3} - 20$

Step 3

Solve for $m$ .

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Step 3.1

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

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Step 3.1.1

Subtract $\frac{10 m}{3}$ from both sides of the equation.

$2 m - \frac{10 m}{3} = - 20$

Step 3.1.2

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

$2 m \cdot \frac{3}{3} - \frac{10 m}{3} = - 20$

Step 3.1.3

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

$\frac{2 m \cdot 3}{3} - \frac{10 m}{3} = - 20$

Step 3.1.4

Combine the numerators over the common denominator.

$\frac{2 m \cdot 3 - 10 m}{3} = - 20$

Step 3.1.5

Simplify the numerator.

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Step 3.1.5.1

Factor $2 m$ out of $2 m \cdot 3 - 10 m$ .

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Step 3.1.5.1.1

Factor $2 m$ out of $2 m \cdot 3$ .

$\frac{2 m (3) - 10 m}{3} = - 20$

Step 3.1.5.1.2

Factor $2 m$ out of $- 10 m$ .

$\frac{2 m (3) + 2 m (- 5)}{3} = - 20$

Step 3.1.5.1.3

Factor $2 m$ out of $2 m (3) + 2 m (- 5)$ .

$\frac{2 m (3 - 5)}{3} = - 20$

Step 3.1.5.2

Subtract $5$ from $3$ .

$\frac{2 m \cdot - 2}{3} = - 20$

Step 3.1.5.3

Multiply $- 2$ by $2$ .

$\frac{- 4 m}{3} = - 20$

Step 3.1.6

Move the negative in front of the fraction.

$- \frac{4 m}{3} = - 20$

Step 3.2

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

$- \frac{3}{4} (- \frac{4 m}{3}) = - \frac{3}{4} \cdot - 20$

Step 3.3

Simplify both sides of the equation.

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Step 3.3.1

Simplify the left side.

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Step 3.3.1.1

Simplify $- \frac{3}{4} (- \frac{4 m}{3})$ .

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Step 3.3.1.1.1

Cancel the common factor of $3$ .

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Step 3.3.1.1.1.1

Move the leading negative in $- \frac{3}{4}$ into the numerator.

$\frac{- 3}{4} (- \frac{4 m}{3}) = - \frac{3}{4} \cdot - 20$

Step 3.3.1.1.1.2

Move the leading negative in $- \frac{4 m}{3}$ into the numerator.

$\frac{- 3}{4} \cdot \frac{- 4 m}{3} = - \frac{3}{4} \cdot - 20$

Step 3.3.1.1.1.3

Factor $3$ out of $- 3$ .

$\frac{3 (- 1)}{4} \cdot \frac{- 4 m}{3} = - \frac{3}{4} \cdot - 20$

Step 3.3.1.1.1.4

Cancel the common factor.

$\frac{3 \cdot - 1}{4} \cdot \frac{- 4 m}{3} = - \frac{3}{4} \cdot - 20$

Step 3.3.1.1.1.5

Rewrite the expression.

$\frac{- 1}{4} (- 4 m) = - \frac{3}{4} \cdot - 20$

Step 3.3.1.1.2

Cancel the common factor of $4$ .

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Step 3.3.1.1.2.1

Factor $4$ out of $- 4 m$ .

$\frac{- 1}{4} (4 (- m)) = - \frac{3}{4} \cdot - 20$

Step 3.3.1.1.2.2

Cancel the common factor.

$\frac{- 1}{4} (4 (- m)) = - \frac{3}{4} \cdot - 20$

Step 3.3.1.1.2.3

Rewrite the expression.

$- - m = - \frac{3}{4} \cdot - 20$

Step 3.3.1.1.3

Multiply.

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Step 3.3.1.1.3.1

Multiply $- 1$ by $- 1$ .

$1 m = - \frac{3}{4} \cdot - 20$

Step 3.3.1.1.3.2

Multiply $m$ by $1$ .

$m = - \frac{3}{4} \cdot - 20$

Step 3.3.2

Simplify the right side.

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Step 3.3.2.1

Simplify $- \frac{3}{4} \cdot - 20$ .

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Step 3.3.2.1.1

Cancel the common factor of $4$ .

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Step 3.3.2.1.1.1

Move the leading negative in $- \frac{3}{4}$ into the numerator.

$m = \frac{- 3}{4} \cdot - 20$

Step 3.3.2.1.1.2

Factor $4$ out of $- 20$ .

$m = \frac{- 3}{4} \cdot (4 (- 5))$

Step 3.3.2.1.1.3

Cancel the common factor.

$m = \frac{- 3}{4} \cdot (4 \cdot - 5)$

Step 3.3.2.1.1.4

Rewrite the expression.

$m = - 3 \cdot - 5$

Step 3.3.2.1.2

Multiply $- 3$ by $- 5$ .

$m = 15$