Algebra Examples

$\frac{2}{3} (m + 7) = 6$

Step 1

Multiply both sides of the equation by $\frac{3}{2}$ .

$\frac{3}{2} (\frac{2}{3} \cdot (m + 7)) = \frac{3}{2} \cdot 6$

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 $\frac{3}{2} (\frac{2}{3} \cdot (m + 7))$ .

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Step 2.1.1.1

Apply the distributive property.

$\frac{3}{2} (\frac{2}{3} m + \frac{2}{3} \cdot 7) = \frac{3}{2} \cdot 6$

Step 2.1.1.2

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

$\frac{3}{2} (\frac{2 m}{3} + \frac{2}{3} \cdot 7) = \frac{3}{2} \cdot 6$

Step 2.1.1.3

Multiply $\frac{2}{3} \cdot 7$ .

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Step 2.1.1.3.1

Combine $\frac{2}{3}$ and $7$ .

$\frac{3}{2} (\frac{2 m}{3} + \frac{2 \cdot 7}{3}) = \frac{3}{2} \cdot 6$

Step 2.1.1.3.2

Multiply $2$ by $7$ .

$\frac{3}{2} (\frac{2 m}{3} + \frac{14}{3}) = \frac{3}{2} \cdot 6$

Step 2.1.1.4

Apply the distributive property.

$\frac{3}{2} \cdot \frac{2 m}{3} + \frac{3}{2} \cdot \frac{14}{3} = \frac{3}{2} \cdot 6$

Step 2.1.1.5

Cancel the common factor of $3$ .

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Step 2.1.1.5.1

Cancel the common factor.

$\frac{3}{2} \cdot \frac{2 m}{3} + \frac{3}{2} \cdot \frac{14}{3} = \frac{3}{2} \cdot 6$

Step 2.1.1.5.2

Rewrite the expression.

$\frac{1}{2} (2 m) + \frac{3}{2} \cdot \frac{14}{3} = \frac{3}{2} \cdot 6$

Step 2.1.1.6

Cancel the common factor of $2$ .

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Step 2.1.1.6.1

Factor $2$ out of $2 m$ .

$\frac{1}{2} (2 (m)) + \frac{3}{2} \cdot \frac{14}{3} = \frac{3}{2} \cdot 6$

Step 2.1.1.6.2

Cancel the common factor.

$\frac{1}{2} (2 m) + \frac{3}{2} \cdot \frac{14}{3} = \frac{3}{2} \cdot 6$

Step 2.1.1.6.3

Rewrite the expression.

$m + \frac{3}{2} \cdot \frac{14}{3} = \frac{3}{2} \cdot 6$

Step 2.1.1.7

Cancel the common factor of $3$ .

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Step 2.1.1.7.1

Cancel the common factor.

$m + \frac{3}{2} \cdot \frac{14}{3} = \frac{3}{2} \cdot 6$

Step 2.1.1.7.2

Rewrite the expression.

$m + \frac{1}{2} \cdot 14 = \frac{3}{2} \cdot 6$

Step 2.1.1.8

Cancel the common factor of $2$ .

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Step 2.1.1.8.1

Factor $2$ out of $14$ .

$m + \frac{1}{2} \cdot (2 (7)) = \frac{3}{2} \cdot 6$

Step 2.1.1.8.2

Cancel the common factor.

$m + \frac{1}{2} \cdot (2 \cdot 7) = \frac{3}{2} \cdot 6$

Step 2.1.1.8.3

Rewrite the expression.

$m + 7 = \frac{3}{2} \cdot 6$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $\frac{3}{2} \cdot 6$ .

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Step 2.2.1.1

Cancel the common factor of $2$ .

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Step 2.2.1.1.1

Factor $2$ out of $6$ .

$m + 7 = \frac{3}{2} \cdot (2 (3))$

Step 2.2.1.1.2

Cancel the common factor.

$m + 7 = \frac{3}{2} \cdot (2 \cdot 3)$

Step 2.2.1.1.3

Rewrite the expression.

$m + 7 = 3 \cdot 3$

Step 2.2.1.2

Multiply $3$ by $3$ .

$m + 7 = 9$

Step 3

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

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Step 3.1

Subtract $7$ from both sides of the equation.

$m = 9 - 7$

Step 3.2

Subtract $7$ from $9$ .

$m = 2$