Finite Math Examples

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

Step 1

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

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Step 1.1

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

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

Step 1.2

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

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

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

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

Step 1.3.2

Multiply $2$ by $3$ .

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

Step 1.3.3

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

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

Step 1.3.4

Multiply $3$ by $2$ .

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

Step 1.4

Combine the numerators over the common denominator.

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

Step 1.5

Simplify each term.

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Step 1.5.1

Simplify the numerator.

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Step 1.5.1.1

Factor $x$ out of $x \cdot 3 + 2 x \cdot 2$ .

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Step 1.5.1.1.1

Factor $x$ out of $x \cdot 3$ .

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

Step 1.5.1.1.2

Factor $x$ out of $2 x \cdot 2$ .

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

Step 1.5.1.1.3

Factor $x$ out of $x (3) + x (2 \cdot 2)$ .

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

Step 1.5.1.2

Multiply $2$ by $2$ .

$\frac{x (3 + 4)}{6} + 3 = x + 3$

Step 1.5.1.3

Add $3$ and $4$ .

$\frac{x \cdot 7}{6} + 3 = x + 3$

Step 1.5.2

Move $7$ to the left of $x$ .

$\frac{7 x}{6} + 3 = x + 3$

Step 2

Move all terms containing $x$ to the left side of the equation.

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Step 2.1

Subtract $x$ from both sides of the equation.

$\frac{7 x}{6} + 3 - x = 3$

Step 2.2

To write $- x$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$\frac{7 x}{6} - x \cdot \frac{6}{6} + 3 = 3$

Step 2.3

Combine $- x$ and $\frac{6}{6}$ .

$\frac{7 x}{6} + \frac{- x \cdot 6}{6} + 3 = 3$

Step 2.4

Combine the numerators over the common denominator.

$\frac{7 x - x \cdot 6}{6} + 3 = 3$

Step 2.5

Simplify each term.

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Step 2.5.1

Simplify the numerator.

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Step 2.5.1.1

Factor $x$ out of $7 x - x \cdot 6$ .

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Step 2.5.1.1.1

Factor $x$ out of $7 x$ .

$\frac{x \cdot 7 - x \cdot 6}{6} + 3 = 3$

Step 2.5.1.1.2

Factor $x$ out of $- x \cdot 6$ .

$\frac{x \cdot 7 + x (- 1 \cdot 6)}{6} + 3 = 3$

Step 2.5.1.1.3

Factor $x$ out of $x \cdot 7 + x (- 1 \cdot 6)$ .

$\frac{x (7 - 1 \cdot 6)}{6} + 3 = 3$

Step 2.5.1.2

Multiply $- 1$ by $6$ .

$\frac{x (7 - 6)}{6} + 3 = 3$

Step 2.5.1.3

Subtract $6$ from $7$ .

$\frac{x \cdot 1}{6} + 3 = 3$

Step 2.5.2

Multiply $x$ by $1$ .

$\frac{x}{6} + 3 = 3$

Step 3

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

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Step 3.1

Subtract $3$ from both sides of the equation.

$\frac{x}{6} = 3 - 3$

Step 3.2

Subtract $3$ from $3$ .

$\frac{x}{6} = 0$

Step 4

Set the numerator equal to zero.

$x = 0$