Algebra Examples

$\frac{5}{8} = \frac{1}{2} (a + 2)$

Step 1

Rewrite the equation as $\frac{1}{2} \cdot (a + 2) = \frac{5}{8}$ .

$\frac{1}{2} \cdot (a + 2) = \frac{5}{8}$

Step 2

Multiply both sides of the equation by $2$ .

$2 (\frac{1}{2} \cdot (a + 2)) = 2 (\frac{5}{8})$

Step 3

Simplify both sides of the equation.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Simplify $2 (\frac{1}{2} \cdot (a + 2))$ .

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Step 3.1.1.1

Apply the distributive property.

$2 (\frac{1}{2} a + \frac{1}{2} \cdot 2) = 2 (\frac{5}{8})$

Step 3.1.1.2

Combine $\frac{1}{2}$ and $a$ .

$2 (\frac{a}{2} + \frac{1}{2} \cdot 2) = 2 (\frac{5}{8})$

Step 3.1.1.3

Cancel the common factor of $2$ .

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Step 3.1.1.3.1

Cancel the common factor.

$2 (\frac{a}{2} + \frac{1}{2} \cdot 2) = 2 (\frac{5}{8})$

Step 3.1.1.3.2

Rewrite the expression.

$2 (\frac{a}{2} + 1) = 2 (\frac{5}{8})$

Step 3.1.1.4

Apply the distributive property.

$2 \frac{a}{2} + 2 \cdot 1 = 2 (\frac{5}{8})$

Step 3.1.1.5

Cancel the common factor of $2$ .

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Step 3.1.1.5.1

Cancel the common factor.

$2 \frac{a}{2} + 2 \cdot 1 = 2 (\frac{5}{8})$

Step 3.1.1.5.2

Rewrite the expression.

$a + 2 \cdot 1 = 2 (\frac{5}{8})$

Step 3.1.1.6

Multiply $2$ by $1$ .

$a + 2 = 2 (\frac{5}{8})$

Step 3.2

Simplify the right side.

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Step 3.2.1

Cancel the common factor of $2$ .

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Step 3.2.1.1

Factor $2$ out of $8$ .

$a + 2 = 2 \frac{5}{2 (4)}$

Step 3.2.1.2

Cancel the common factor.

$a + 2 = 2 \frac{5}{2 \cdot 4}$

Step 3.2.1.3

Rewrite the expression.

$a + 2 = \frac{5}{4}$

Step 4

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

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Step 4.1

Subtract $2$ from both sides of the equation.

$a = \frac{5}{4} - 2$

Step 4.2

To write $- 2$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$a = \frac{5}{4} - 2 \cdot \frac{4}{4}$

Step 4.3

Combine $- 2$ and $\frac{4}{4}$ .

$a = \frac{5}{4} + \frac{- 2 \cdot 4}{4}$

Step 4.4

Combine the numerators over the common denominator.

$a = \frac{5 - 2 \cdot 4}{4}$

Step 4.5

Simplify the numerator.

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Step 4.5.1

Multiply $- 2$ by $4$ .

$a = \frac{5 - 8}{4}$

Step 4.5.2

Subtract $8$ from $5$ .

$a = \frac{- 3}{4}$

Step 4.6

Move the negative in front of the fraction.

$a = - \frac{3}{4}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$a = - \frac{3}{4}$

Decimal Form:

$a = - 0.75$