Basic Math Examples

$\frac{3 r + 8}{9} = \frac{2 r - 12}{2}$

Step 1

Multiply both sides by $9$ .

$\frac{3 r + 8}{9} \cdot 9 = \frac{2 r - 12}{2} \cdot 9$

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 $9$ .

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Step 2.1.1.1

Cancel the common factor.

$\frac{3 r + 8}{9} \cdot 9 = \frac{2 r - 12}{2} \cdot 9$

Step 2.1.1.2

Rewrite the expression.

$3 r + 8 = \frac{2 r - 12}{2} \cdot 9$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $\frac{2 r - 12}{2} \cdot 9$ .

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Step 2.2.1.1

Factor $2$ out of $2 r - 12$ .

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Step 2.2.1.1.1

Factor $2$ out of $2 r$ .

$3 r + 8 = \frac{2 (r) - 12}{2} \cdot 9$

Step 2.2.1.1.2

Factor $2$ out of $- 12$ .

$3 r + 8 = \frac{2 r + 2 \cdot - 6}{2} \cdot 9$

Step 2.2.1.1.3

Factor $2$ out of $2 r + 2 \cdot - 6$ .

$3 r + 8 = \frac{2 (r - 6)}{2} \cdot 9$

Step 2.2.1.2

Cancel the common factor of $2$ .

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Step 2.2.1.2.1

Cancel the common factor.

$3 r + 8 = \frac{2 (r - 6)}{2} \cdot 9$

Step 2.2.1.2.2

Divide $r - 6$ by $1$ .

$3 r + 8 = (r - 6) \cdot 9$

Step 2.2.1.3

Apply the distributive property.

$3 r + 8 = r \cdot 9 - 6 \cdot 9$

Step 2.2.1.4

Simplify the expression.

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Step 2.2.1.4.1

Move $9$ to the left of $r$ .

$3 r + 8 = 9 \cdot r - 6 \cdot 9$

Step 2.2.1.4.2

Multiply $- 6$ by $9$ .

$3 r + 8 = 9 r - 54$

Step 3

Solve for $r$ .

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Step 3.1

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

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Step 3.1.1

Subtract $9 r$ from both sides of the equation.

$3 r + 8 - 9 r = - 54$

Step 3.1.2

Subtract $9 r$ from $3 r$ .

$- 6 r + 8 = - 54$

Step 3.2

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

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Step 3.2.1

Subtract $8$ from both sides of the equation.

$- 6 r = - 54 - 8$

Step 3.2.2

Subtract $8$ from $- 54$ .

$- 6 r = - 62$

Step 3.3

Divide each term in $- 6 r = - 62$ by $- 6$ and simplify.

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Step 3.3.1

Divide each term in $- 6 r = - 62$ by $- 6$ .

$\frac{- 6 r}{- 6} = \frac{- 62}{- 6}$

Step 3.3.2

Simplify the left side.

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Step 3.3.2.1

Cancel the common factor of $- 6$ .

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Step 3.3.2.1.1

Cancel the common factor.

$\frac{- 6 r}{- 6} = \frac{- 62}{- 6}$

Step 3.3.2.1.2

Divide $r$ by $1$ .

$r = \frac{- 62}{- 6}$

Step 3.3.3

Simplify the right side.

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Step 3.3.3.1

Cancel the common factor of $- 62$ and $- 6$ .

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Step 3.3.3.1.1

Factor $- 2$ out of $- 62$ .

$r = \frac{- 2 (31)}{- 6}$

Step 3.3.3.1.2

Cancel the common factors.

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Step 3.3.3.1.2.1

Factor $- 2$ out of $- 6$ .

$r = \frac{- 2 \cdot 31}{- 2 \cdot 3}$

Step 3.3.3.1.2.2

Cancel the common factor.

$r = \frac{- 2 \cdot 31}{- 2 \cdot 3}$

Step 3.3.3.1.2.3

Rewrite the expression.

$r = \frac{31}{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$r = \frac{31}{3}$

Decimal Form:

$r = 10.\overline{3}$

Mixed Number Form:

$r = 10 \frac{1}{3}$