Basic Math Examples

$\frac{4 r + 16}{12} = \frac{3 r - 12}{3}$

Step 1

Cancel the common factor of $4 r + 16$ and $12$ .

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Step 1.1

Factor $4$ out of $4 r$ .

$\frac{4 (r) + 16}{12} = \frac{3 r - 12}{3}$

Step 1.2

Factor $4$ out of $16$ .

$\frac{4 r + 4 \cdot 4}{12} = \frac{3 r - 12}{3}$

Step 1.3

Factor $4$ out of $4 r + 4 \cdot 4$ .

$\frac{4 (r + 4)}{12} = \frac{3 r - 12}{3}$

Step 1.4

Cancel the common factors.

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Step 1.4.1

Factor $4$ out of $12$ .

$\frac{4 (r + 4)}{4 (3)} = \frac{3 r - 12}{3}$

Step 1.4.2

Cancel the common factor.

$\frac{4 (r + 4)}{4 \cdot 3} = \frac{3 r - 12}{3}$

Step 1.4.3

Rewrite the expression.

$\frac{r + 4}{3} = \frac{3 r - 12}{3}$

Step 2

Multiply both sides by $3$ .

$\frac{r + 4}{3} \cdot 3 = \frac{3 r - 12}{3} \cdot 3$

Step 3

Simplify.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Cancel the common factor of $3$ .

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Step 3.1.1.1

Cancel the common factor.

$\frac{r + 4}{3} \cdot 3 = \frac{3 r - 12}{3} \cdot 3$

Step 3.1.1.2

Rewrite the expression.

$r + 4 = \frac{3 r - 12}{3} \cdot 3$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $\frac{3 r - 12}{3} \cdot 3$ .

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Step 3.2.1.1

Factor $3$ out of $3 r - 12$ .

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Step 3.2.1.1.1

Factor $3$ out of $3 r$ .

$r + 4 = \frac{3 (r) - 12}{3} \cdot 3$

Step 3.2.1.1.2

Factor $3$ out of $- 12$ .

$r + 4 = \frac{3 r + 3 \cdot - 4}{3} \cdot 3$

Step 3.2.1.1.3

Factor $3$ out of $3 r + 3 \cdot - 4$ .

$r + 4 = \frac{3 (r - 4)}{3} \cdot 3$

Step 3.2.1.2

Cancel the common factor of $3$ .

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Step 3.2.1.2.1

Cancel the common factor.

$r + 4 = \frac{3 (r - 4)}{3} \cdot 3$

Step 3.2.1.2.2

Rewrite the expression.

$r + 4 = 3 (r - 4)$

Step 3.2.1.3

Apply the distributive property.

$r + 4 = 3 r + 3 \cdot - 4$

Step 3.2.1.4

Multiply $3$ by $- 4$ .

$r + 4 = 3 r - 12$

Step 4

Solve for $r$ .

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Step 4.1

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

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Step 4.1.1

Subtract $3 r$ from both sides of the equation.

$r + 4 - 3 r = - 12$

Step 4.1.2

Subtract $3 r$ from $r$ .

$- 2 r + 4 = - 12$

Step 4.2

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

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Step 4.2.1

Subtract $4$ from both sides of the equation.

$- 2 r = - 12 - 4$

Step 4.2.2

Subtract $4$ from $- 12$ .

$- 2 r = - 16$

Step 4.3

Divide each term in $- 2 r = - 16$ by $- 2$ and simplify.

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Step 4.3.1

Divide each term in $- 2 r = - 16$ by $- 2$ .

$\frac{- 2 r}{- 2} = \frac{- 16}{- 2}$

Step 4.3.2

Simplify the left side.

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Step 4.3.2.1

Cancel the common factor of $- 2$ .

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Step 4.3.2.1.1

Cancel the common factor.

$\frac{- 2 r}{- 2} = \frac{- 16}{- 2}$

Step 4.3.2.1.2

Divide $r$ by $1$ .

$r = \frac{- 16}{- 2}$

Step 4.3.3

Simplify the right side.

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Step 4.3.3.1

Divide $- 16$ by $- 2$ .

$r = 8$