Algebra Examples

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

Step 1

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

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Step 1.1

Subtract $\frac{1}{5} x$ from both sides of the equation.

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

Step 1.2

Subtract $2$ from both sides of the equation.

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

Step 2

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

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Step 2.1

Simplify each term.

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Step 2.1.1

Combine $\frac{1}{6}$ and $x$ .

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

Step 2.1.2

Combine $x$ and $\frac{1}{5}$ .

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

Step 2.2

To write $\frac{x}{6}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

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

Step 2.3

To write $- \frac{x}{5}$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

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

Step 2.4

Write each expression with a common denominator of $30$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.4.1

Multiply $\frac{x}{6}$ by $\frac{5}{5}$ .

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

Step 2.4.2

Multiply $6$ by $5$ .

$\frac{x \cdot 5}{30} - \frac{x}{5} \cdot \frac{6}{6} - 5 - 2 = 0$

Step 2.4.3

Multiply $\frac{x}{5}$ by $\frac{6}{6}$ .

$\frac{x \cdot 5}{30} - \frac{x \cdot 6}{5 \cdot 6} - 5 - 2 = 0$

Step 2.4.4

Multiply $5$ by $6$ .

$\frac{x \cdot 5}{30} - \frac{x \cdot 6}{30} - 5 - 2 = 0$

Step 2.5

Combine the numerators over the common denominator.

$\frac{x \cdot 5 - x \cdot 6}{30} - 5 - 2 = 0$

Step 2.6

Find the common denominator.

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Step 2.6.1

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

$\frac{x \cdot 5 - x \cdot 6}{30} + \frac{- 5}{1} - 2 = 0$

Step 2.6.2

Multiply $\frac{- 5}{1}$ by $\frac{30}{30}$ .

$\frac{x \cdot 5 - x \cdot 6}{30} + \frac{- 5}{1} \cdot \frac{30}{30} - 2 = 0$

Step 2.6.3

Multiply $\frac{- 5}{1}$ by $\frac{30}{30}$ .

$\frac{x \cdot 5 - x \cdot 6}{30} + \frac{- 5 \cdot 30}{30} - 2 = 0$

Step 2.6.4

Write $- 2$ as a fraction with denominator $1$ .

$\frac{x \cdot 5 - x \cdot 6}{30} + \frac{- 5 \cdot 30}{30} + \frac{- 2}{1} = 0$

Step 2.6.5

Multiply $\frac{- 2}{1}$ by $\frac{30}{30}$ .

$\frac{x \cdot 5 - x \cdot 6}{30} + \frac{- 5 \cdot 30}{30} + \frac{- 2}{1} \cdot \frac{30}{30} = 0$

Step 2.6.6

Multiply $\frac{- 2}{1}$ by $\frac{30}{30}$ .

$\frac{x \cdot 5 - x \cdot 6}{30} + \frac{- 5 \cdot 30}{30} + \frac{- 2 \cdot 30}{30} = 0$

Step 2.7

Combine the numerators over the common denominator.

$\frac{x \cdot 5 - x \cdot 6 - 5 \cdot 30 - 2 \cdot 30}{30} = 0$

Step 2.8

Simplify each term.

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Step 2.8.1

Move $5$ to the left of $x$ .

$\frac{5 \cdot x - x \cdot 6 - 5 \cdot 30 - 2 \cdot 30}{30} = 0$

Step 2.8.2

Multiply $6$ by $- 1$ .

$\frac{5 x - 6 x - 5 \cdot 30 - 2 \cdot 30}{30} = 0$

Step 2.8.3

Multiply $- 5$ by $30$ .

$\frac{5 x - 6 x - 150 - 2 \cdot 30}{30} = 0$

Step 2.8.4

Multiply $- 2$ by $30$ .

$\frac{5 x - 6 x - 150 - 60}{30} = 0$

Step 2.9

Subtract $6 x$ from $5 x$ .

$\frac{- x - 150 - 60}{30} = 0$

Step 2.10

Subtract $60$ from $- 150$ .

$\frac{- x - 210}{30} = 0$

Step 2.11

Factor $- 1$ out of $- x$ .

$\frac{- (x) - 210}{30} = 0$

Step 2.12

Rewrite $- 210$ as $- 1 (210)$ .

$\frac{- (x) - 1 (210)}{30} = 0$

Step 2.13

Factor $- 1$ out of $- (x) - 1 (210)$ .

$\frac{- (x + 210)}{30} = 0$

Step 2.14

Rewrite $- (x + 210)$ as $- 1 (x + 210)$ .

$\frac{- 1 (x + 210)}{30} = 0$

Step 2.15

Move the negative in front of the fraction.

$- \frac{x + 210}{30} = 0$