Write as a Set of Linear Factors 1/2x-5=1/3x+6

$\frac{1}{2} x - 5 = \frac{1}{3} x + 6$

Step 1

Move all the expressions to the left side of the equation.

Subtract $\frac{1}{3} x$ from both sides of the equation.

$\frac{1}{2} x - 5 - \frac{1}{3} x = 6$

Subtract $6$ from both sides of the equation.

$\frac{1}{2} x - 5 - \frac{1}{3} x - 6 = 0$

Step 2

Simplify $\frac{1}{2} x - 5 - \frac{1}{3} x - 6$ .

Simplify each term.

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

$\frac{x}{2} - 5 - \frac{1}{3} x - 6 = 0$

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

$\frac{x}{2} - 5 - \frac{x}{3} - 6 = 0$

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

$\frac{x}{2} \cdot \frac{3}{3} - \frac{x}{3} - 5 - 6 = 0$

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

$\frac{x}{2} \cdot \frac{3}{3} - \frac{x}{3} \cdot \frac{2}{2} - 5 - 6 = 0$

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

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

$\frac{x \cdot 3}{2 \cdot 3} - \frac{x}{3} \cdot \frac{2}{2} - 5 - 6 = 0$

Multiply $2$ by $3$ .

$\frac{x \cdot 3}{6} - \frac{x}{3} \cdot \frac{2}{2} - 5 - 6 = 0$

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

$\frac{x \cdot 3}{6} - \frac{x \cdot 2}{3 \cdot 2} - 5 - 6 = 0$

Multiply $3$ by $2$ .

$\frac{x \cdot 3}{6} - \frac{x \cdot 2}{6} - 5 - 6 = 0$

Combine the numerators over the common denominator.

$\frac{x \cdot 3 - x \cdot 2}{6} - 5 - 6 = 0$

Find the common denominator.

Write $- 5$ as a fraction with denominator $1$ .

$\frac{x \cdot 3 - x \cdot 2}{6} + \frac{- 5}{1} - 6 = 0$

Multiply $\frac{- 5}{1}$ by $\frac{6}{6}$ .

$\frac{x \cdot 3 - x \cdot 2}{6} + \frac{- 5}{1} \cdot \frac{6}{6} - 6 = 0$

Multiply $\frac{- 5}{1}$ by $\frac{6}{6}$ .

$\frac{x \cdot 3 - x \cdot 2}{6} + \frac{- 5 \cdot 6}{6} - 6 = 0$

Write $- 6$ as a fraction with denominator $1$ .

$\frac{x \cdot 3 - x \cdot 2}{6} + \frac{- 5 \cdot 6}{6} + \frac{- 6}{1} = 0$

Multiply $\frac{- 6}{1}$ by $\frac{6}{6}$ .

$\frac{x \cdot 3 - x \cdot 2}{6} + \frac{- 5 \cdot 6}{6} + \frac{- 6}{1} \cdot \frac{6}{6} = 0$

Multiply $\frac{- 6}{1}$ by $\frac{6}{6}$ .

$\frac{x \cdot 3 - x \cdot 2}{6} + \frac{- 5 \cdot 6}{6} + \frac{- 6 \cdot 6}{6} = 0$

Combine the numerators over the common denominator.

$\frac{x \cdot 3 - x \cdot 2 - 5 \cdot 6 - 6 \cdot 6}{6} = 0$

Simplify each term.

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

$\frac{3 \cdot x - x \cdot 2 - 5 \cdot 6 - 6 \cdot 6}{6} = 0$

Multiply $2$ by $- 1$ .

$\frac{3 x - 2 x - 5 \cdot 6 - 6 \cdot 6}{6} = 0$

Multiply $- 5$ by $6$ .

$\frac{3 x - 2 x - 30 - 6 \cdot 6}{6} = 0$

Multiply $- 6$ by $6$ .

$\frac{3 x - 2 x - 30 - 36}{6} = 0$

Subtract $2 x$ from $3 x$ .

$\frac{x - 30 - 36}{6} = 0$

Subtract $36$ from $- 30$ .

$\frac{x - 66}{6} = 0$

Write as a Set of Linear Factors 1/2x-5=1/3x+6

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