Algebra Examples

$\frac{1}{3} (15 m - 12) = - 5 (m - 2)$

Step 1

Simplify $\frac{1}{3} \cdot (15 m - 12)$ .

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Step 1.1

Rewrite.

$0 + 0 + \frac{1}{3} \cdot (15 m - 12) = - 5 (m - 2)$

Step 1.2

Simplify by adding zeros.

$\frac{1}{3} \cdot (15 m - 12) = - 5 (m - 2)$

Step 1.3

Apply the distributive property.

$\frac{1}{3} (15 m) + \frac{1}{3} \cdot - 12 = - 5 (m - 2)$

Step 1.4

Cancel the common factor of $3$ .

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Step 1.4.1

Factor $3$ out of $15 m$ .

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

Step 1.4.2

Cancel the common factor.

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

Step 1.4.3

Rewrite the expression.

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

Step 1.5

Cancel the common factor of $3$ .

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Step 1.5.1

Factor $3$ out of $- 12$ .

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

Step 1.5.2

Cancel the common factor.

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

Step 1.5.3

Rewrite the expression.

$5 m - 4 = - 5 (m - 2)$

Step 2

Simplify $- 5 (m - 2)$ .

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Step 2.1

Apply the distributive property.

$5 m - 4 = - 5 m - 5 \cdot - 2$

Step 2.2

Multiply $- 5$ by $- 2$ .

$5 m - 4 = - 5 m + 10$

Step 3

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

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Step 3.1

Add $5 m$ to both sides of the equation.

$5 m - 4 + 5 m = 10$

Step 3.2

Add $5 m$ and $5 m$ .

$10 m - 4 = 10$

Step 4

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

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Step 4.1

Add $4$ to both sides of the equation.

$10 m = 10 + 4$

Step 4.2

Add $10$ and $4$ .

$10 m = 14$

Step 5

Divide each term in $10 m = 14$ by $10$ and simplify.

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Step 5.1

Divide each term in $10 m = 14$ by $10$ .

$\frac{10 m}{10} = \frac{14}{10}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $10$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{10 m}{10} = \frac{14}{10}$

Step 5.2.1.2

Divide $m$ by $1$ .

$m = \frac{14}{10}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Cancel the common factor of $14$ and $10$ .

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Step 5.3.1.1

Factor $2$ out of $14$ .

$m = \frac{2 (7)}{10}$

Step 5.3.1.2

Cancel the common factors.

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Step 5.3.1.2.1

Factor $2$ out of $10$ .

$m = \frac{2 \cdot 7}{2 \cdot 5}$

Step 5.3.1.2.2

Cancel the common factor.

$m = \frac{2 \cdot 7}{2 \cdot 5}$

Step 5.3.1.2.3

Rewrite the expression.

$m = \frac{7}{5}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$m = \frac{7}{5}$

Decimal Form:

$m = 1.4$

Mixed Number Form:

$m = 1 \frac{2}{5}$