Precalculus Examples

$\frac{1}{3} (a + 5) = \frac{7}{2}$

Step 1

Multiply both sides of the equation by $3$ .

$3 (\frac{1}{3} \cdot (a + 5)) = 3 (\frac{7}{2})$

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 $3 (\frac{1}{3} \cdot (a + 5))$ .

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Step 2.1.1.1

Apply the distributive property.

$3 (\frac{1}{3} a + \frac{1}{3} \cdot 5) = 3 (\frac{7}{2})$

Step 2.1.1.2

Combine $\frac{1}{3}$ and $a$ .

$3 (\frac{a}{3} + \frac{1}{3} \cdot 5) = 3 (\frac{7}{2})$

Step 2.1.1.3

Combine $\frac{1}{3}$ and $5$ .

$3 (\frac{a}{3} + \frac{5}{3}) = 3 (\frac{7}{2})$

Step 2.1.1.4

Apply the distributive property.

$3 \frac{a}{3} + 3 (\frac{5}{3}) = 3 (\frac{7}{2})$

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.

$3 \frac{a}{3} + 3 (\frac{5}{3}) = 3 (\frac{7}{2})$

Step 2.1.1.5.2

Rewrite the expression.

$a + 3 (\frac{5}{3}) = 3 (\frac{7}{2})$

Step 2.1.1.6

Cancel the common factor of $3$ .

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Step 2.1.1.6.1

Cancel the common factor.

$a + 3 (\frac{5}{3}) = 3 (\frac{7}{2})$

Step 2.1.1.6.2

Rewrite the expression.

$a + 5 = 3 (\frac{7}{2})$

Step 2.2

Simplify the right side.

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Step 2.2.1

Multiply $3 (\frac{7}{2})$ .

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Step 2.2.1.1

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

$a + 5 = \frac{3 \cdot 7}{2}$

Step 2.2.1.2

Multiply $3$ by $7$ .

$a + 5 = \frac{21}{2}$

Step 3

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

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Step 3.1

Subtract $5$ from both sides of the equation.

$a = \frac{21}{2} - 5$

Step 3.2

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

$a = \frac{21}{2} - 5 \cdot \frac{2}{2}$

Step 3.3

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

$a = \frac{21}{2} + \frac{- 5 \cdot 2}{2}$

Step 3.4

Combine the numerators over the common denominator.

$a = \frac{21 - 5 \cdot 2}{2}$

Step 3.5

Simplify the numerator.

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Step 3.5.1

Multiply $- 5$ by $2$ .

$a = \frac{21 - 10}{2}$

Step 3.5.2

Subtract $10$ from $21$ .

$a = \frac{11}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$a = \frac{11}{2}$

Decimal Form:

$a = 5.5$

Mixed Number Form:

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