Algebra Examples

$\frac{1}{2} (x + \frac{5}{2}) = \frac{15}{4}$

Step 1

Multiply both sides of the equation by $2$ .

$2 (\frac{1}{2} \cdot (x + \frac{5}{2})) = 2 (\frac{15}{4})$

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 $2 (\frac{1}{2} \cdot (x + \frac{5}{2}))$ .

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Step 2.1.1.1

Apply the distributive property.

$2 (\frac{1}{2} x + \frac{1}{2} \cdot \frac{5}{2}) = 2 (\frac{15}{4})$

Step 2.1.1.2

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

$2 (\frac{x}{2} + \frac{1}{2} \cdot \frac{5}{2}) = 2 (\frac{15}{4})$

Step 2.1.1.3

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

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Step 2.1.1.3.1

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

$2 (\frac{x}{2} + \frac{5}{2 \cdot 2}) = 2 (\frac{15}{4})$

Step 2.1.1.3.2

Multiply $2$ by $2$ .

$2 (\frac{x}{2} + \frac{5}{4}) = 2 (\frac{15}{4})$

Step 2.1.1.4

Apply the distributive property.

$2 \frac{x}{2} + 2 (\frac{5}{4}) = 2 (\frac{15}{4})$

Step 2.1.1.5

Cancel the common factor of $2$ .

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Step 2.1.1.5.1

Cancel the common factor.

$2 \frac{x}{2} + 2 (\frac{5}{4}) = 2 (\frac{15}{4})$

Step 2.1.1.5.2

Rewrite the expression.

$x + 2 (\frac{5}{4}) = 2 (\frac{15}{4})$

Step 2.1.1.6

Cancel the common factor of $2$ .

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Step 2.1.1.6.1

Factor $2$ out of $4$ .

$x + 2 \frac{5}{2 (2)} = 2 (\frac{15}{4})$

Step 2.1.1.6.2

Cancel the common factor.

$x + 2 \frac{5}{2 \cdot 2} = 2 (\frac{15}{4})$

Step 2.1.1.6.3

Rewrite the expression.

$x + \frac{5}{2} = 2 (\frac{15}{4})$

Step 2.2

Simplify the right side.

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Step 2.2.1

Cancel the common factor of $2$ .

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Step 2.2.1.1

Factor $2$ out of $4$ .

$x + \frac{5}{2} = 2 \frac{15}{2 (2)}$

Step 2.2.1.2

Cancel the common factor.

$x + \frac{5}{2} = 2 \frac{15}{2 \cdot 2}$

Step 2.2.1.3

Rewrite the expression.

$x + \frac{5}{2} = \frac{15}{2}$

Step 3

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

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Step 3.1

Subtract $\frac{5}{2}$ from both sides of the equation.

$x = \frac{15}{2} - \frac{5}{2}$

Step 3.2

Combine the numerators over the common denominator.

$x = \frac{15 - 5}{2}$

Step 3.3

Subtract $5$ from $15$ .

$x = \frac{10}{2}$

Step 3.4

Divide $10$ by $2$ .

$x = 5$