Finite Math Examples

$\frac{x + 2}{2} - \frac{x}{3} = 5$

Step 1

Simplify $\frac{x + 2}{2} - \frac{x}{3}$ .

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Step 1.1

To write $\frac{x + 2}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{x + 2}{2} \cdot \frac{3}{3} - \frac{x}{3} = 5$

Step 1.2

To write $- \frac{x}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{x + 2}{2} \cdot \frac{3}{3} - \frac{x}{3} \cdot \frac{2}{2} = 5$

Step 1.3

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.3.1

Multiply $\frac{x + 2}{2}$ by $\frac{3}{3}$ .

$\frac{(x + 2) \cdot 3}{2 \cdot 3} - \frac{x}{3} \cdot \frac{2}{2} = 5$

Step 1.3.2

Multiply $2$ by $3$ .

$\frac{(x + 2) \cdot 3}{6} - \frac{x}{3} \cdot \frac{2}{2} = 5$

Step 1.3.3

Multiply $\frac{x}{3}$ by $\frac{2}{2}$ .

$\frac{(x + 2) \cdot 3}{6} - \frac{x \cdot 2}{3 \cdot 2} = 5$

Step 1.3.4

Multiply $3$ by $2$ .

$\frac{(x + 2) \cdot 3}{6} - \frac{x \cdot 2}{6} = 5$

Step 1.4

Combine the numerators over the common denominator.

$\frac{(x + 2) \cdot 3 - x \cdot 2}{6} = 5$

Step 1.5

Simplify the numerator.

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Step 1.5.1

Apply the distributive property.

$\frac{x \cdot 3 + 2 \cdot 3 - x \cdot 2}{6} = 5$

Step 1.5.2

Move $3$ to the left of $x$ .

$\frac{3 \cdot x + 2 \cdot 3 - x \cdot 2}{6} = 5$

Step 1.5.3

Multiply $2$ by $3$ .

$\frac{3 \cdot x + 6 - x \cdot 2}{6} = 5$

Step 1.5.4

Multiply $2$ by $- 1$ .

$\frac{3 x + 6 - 2 x}{6} = 5$

Step 1.5.5

Subtract $2 x$ from $3 x$ .

$\frac{x + 6}{6} = 5$

Step 2

Multiply both sides of the equation by $6$ .

$6 \frac{x + 6}{6} = 6 \cdot 5$

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

Cancel the common factor of $6$ .

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Step 3.1.1.1

Cancel the common factor.

$6 \frac{x + 6}{6} = 6 \cdot 5$

Step 3.1.1.2

Rewrite the expression.

$x + 6 = 6 \cdot 5$

Step 3.2

Simplify the right side.

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Step 3.2.1

Multiply $6$ by $5$ .

$x + 6 = 30$

Step 4

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

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Step 4.1

Subtract $6$ from both sides of the equation.

$x = 30 - 6$

Step 4.2

Subtract $6$ from $30$ .

$x = 24$