Basic Math Examples

$(r + \frac{3}{2}) = \frac{4 r - 5}{9}$

Step 1

Multiply both sides by $9$ .

$(r + \frac{3}{2}) \cdot 9 = \frac{4 r - 5}{9} \cdot 9$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $(r + \frac{3}{2}) \cdot 9$ .

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Step 2.1.1.1

Apply the distributive property.

$r \cdot 9 + \frac{3}{2} \cdot 9 = \frac{4 r - 5}{9} \cdot 9$

Step 2.1.1.2

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

$9 \cdot r + \frac{3}{2} \cdot 9 = \frac{4 r - 5}{9} \cdot 9$

Step 2.1.1.3

Multiply $\frac{3}{2} \cdot 9$ .

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Step 2.1.1.3.1

Combine $\frac{3}{2}$ and $9$ .

$9 \cdot r + \frac{3 \cdot 9}{2} = \frac{4 r - 5}{9} \cdot 9$

Step 2.1.1.3.2

Multiply $3$ by $9$ .

$9 \cdot r + \frac{27}{2} = \frac{4 r - 5}{9} \cdot 9$

$9 r + \frac{27}{2} = \frac{4 r - 5}{9} \cdot 9$

Step 2.2

Simplify the right side.

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Step 2.2.1

Cancel the common factor of $9$ .

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Step 2.2.1.1

Cancel the common factor.

$9 r + \frac{27}{2} = \frac{4 r - 5}{9} \cdot 9$

Step 2.2.1.2

Rewrite the expression.

$9 r + \frac{27}{2} = 4 r - 5$

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 $4 r$ from both sides of the equation.

$9 r + \frac{27}{2} - 4 r = - 5$

Step 3.1.2

Subtract $4 r$ from $9 r$ .

$5 r + \frac{27}{2} = - 5$

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 $\frac{27}{2}$ from both sides of the equation.

$5 r = - 5 - \frac{27}{2}$

Step 3.2.2

To write $- 5$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$5 r = - 5 \cdot \frac{2}{2} - \frac{27}{2}$

Step 3.2.3

Combine $- 5$ and $\frac{2}{2}$ .

$5 r = \frac{- 5 \cdot 2}{2} - \frac{27}{2}$

Step 3.2.4

Combine the numerators over the common denominator.

$5 r = \frac{- 5 \cdot 2 - 27}{2}$

Step 3.2.5

Simplify the numerator.

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Step 3.2.5.1

Multiply $- 5$ by $2$ .

$5 r = \frac{- 10 - 27}{2}$

Step 3.2.5.2

Subtract $27$ from $- 10$ .

$5 r = \frac{- 37}{2}$

Step 3.2.6

Move the negative in front of the fraction.

$5 r = - \frac{37}{2}$

Step 3.3

Divide each term in $5 r = - \frac{37}{2}$ by $5$ and simplify.

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Step 3.3.1

Divide each term in $5 r = - \frac{37}{2}$ by $5$ .

$\frac{5 r}{5} = \frac{- \frac{37}{2}}{5}$

Step 3.3.2

Simplify the left side.

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Step 3.3.2.1

Cancel the common factor of $5$ .

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Step 3.3.2.1.1

Cancel the common factor.

$\frac{5 r}{5} = \frac{- \frac{37}{2}}{5}$

Step 3.3.2.1.2

Divide $r$ by $1$ .

$r = \frac{- \frac{37}{2}}{5}$

Step 3.3.3

Simplify the right side.

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Step 3.3.3.1

Multiply the numerator by the reciprocal of the denominator.

$r = - \frac{37}{2} \cdot \frac{1}{5}$

Step 3.3.3.2

Multiply $- \frac{37}{2} \cdot \frac{1}{5}$ .

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Step 3.3.3.2.1

Multiply $\frac{1}{5}$ by $\frac{37}{2}$ .

$r = - \frac{37}{5 \cdot 2}$

Step 3.3.3.2.2

Multiply $5$ by $2$ .

$r = - \frac{37}{10}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$r = - \frac{37}{10}$

Decimal Form:

$r = - 3.7$

Mixed Number Form:

$r = - 3 \frac{7}{10}$