Algebra Examples

$\frac{3}{10} x - \frac{1}{5} = - 2$

Step 1

Combine $\frac{3}{10}$ and $x$ .

$\frac{3 x}{10} - \frac{1}{5} = - 2$

Step 2

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

Tap for more steps...

Step 2.1

Add $\frac{1}{5}$ to both sides of the equation.

$\frac{3 x}{10} = - 2 + \frac{1}{5}$

Step 2.2

To write $- 2$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{3 x}{10} = - 2 \cdot \frac{5}{5} + \frac{1}{5}$

Step 2.3

Combine $- 2$ and $\frac{5}{5}$ .

$\frac{3 x}{10} = \frac{- 2 \cdot 5}{5} + \frac{1}{5}$

Step 2.4

Combine the numerators over the common denominator.

$\frac{3 x}{10} = \frac{- 2 \cdot 5 + 1}{5}$

Step 2.5

Simplify the numerator.

Tap for more steps...

Step 2.5.1

Multiply $- 2$ by $5$ .

$\frac{3 x}{10} = \frac{- 10 + 1}{5}$

Step 2.5.2

Add $- 10$ and $1$ .

$\frac{3 x}{10} = \frac{- 9}{5}$

Step 2.6

Move the negative in front of the fraction.

$\frac{3 x}{10} = - \frac{9}{5}$

Step 3

Multiply both sides of the equation by $\frac{10}{3}$ .

$\frac{10}{3} \cdot \frac{3 x}{10} = \frac{10}{3} (- \frac{9}{5})$

Step 4

Simplify both sides of the equation.

Tap for more steps...

Step 4.1

Simplify the left side.

Tap for more steps...

Step 4.1.1

Simplify $\frac{10}{3} \cdot \frac{3 x}{10}$ .

Tap for more steps...

Step 4.1.1.1

Cancel the common factor of $10$ .

Tap for more steps...

Step 4.1.1.1.1

Cancel the common factor.

$\frac{10}{3} \cdot \frac{3 x}{10} = \frac{10}{3} (- \frac{9}{5})$

Step 4.1.1.1.2

Rewrite the expression.

$\frac{1}{3} (3 x) = \frac{10}{3} (- \frac{9}{5})$

Step 4.1.1.2

Cancel the common factor of $3$ .

Tap for more steps...

Step 4.1.1.2.1

Factor $3$ out of $3 x$ .

$\frac{1}{3} (3 (x)) = \frac{10}{3} (- \frac{9}{5})$

Step 4.1.1.2.2

Cancel the common factor.

$\frac{1}{3} (3 x) = \frac{10}{3} (- \frac{9}{5})$

Step 4.1.1.2.3

Rewrite the expression.

$x = \frac{10}{3} (- \frac{9}{5})$

Step 4.2

Simplify the right side.

Tap for more steps...

Step 4.2.1

Simplify $\frac{10}{3} (- \frac{9}{5})$ .

Tap for more steps...

Step 4.2.1.1

Cancel the common factor of $5$ .

Tap for more steps...

Step 4.2.1.1.1

Move the leading negative in $- \frac{9}{5}$ into the numerator.

$x = \frac{10}{3} \cdot \frac{- 9}{5}$

Step 4.2.1.1.2

Factor $5$ out of $10$ .

$x = \frac{5 (2)}{3} \cdot \frac{- 9}{5}$

Step 4.2.1.1.3

Cancel the common factor.

$x = \frac{5 \cdot 2}{3} \cdot \frac{- 9}{5}$

Step 4.2.1.1.4

Rewrite the expression.

$x = \frac{2}{3} \cdot - 9$

Step 4.2.1.2

Cancel the common factor of $3$ .

Tap for more steps...

Step 4.2.1.2.1

Factor $3$ out of $- 9$ .

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

Step 4.2.1.2.2

Cancel the common factor.

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

Step 4.2.1.2.3

Rewrite the expression.

$x = 2 \cdot - 3$

Step 4.2.1.3

Multiply $2$ by $- 3$ .

$x = - 6$