Algebra Examples

$20 - \frac{x}{3} = \frac{x}{2}$

Step 1

Multiply both sides by $2$ .

$(20 - \frac{x}{3}) \cdot 2 = \frac{x}{2} \cdot 2$

Step 2

Simplify.

Tap for more steps...

Step 2.1

Simplify the left side.

Tap for more steps...

Step 2.1.1

Simplify $(20 - \frac{x}{3}) \cdot 2$ .

Tap for more steps...

Step 2.1.1.1

Apply the distributive property.

$20 \cdot 2 - \frac{x}{3} \cdot 2 = \frac{x}{2} \cdot 2$

Step 2.1.1.2

Multiply $20$ by $2$ .

$40 - \frac{x}{3} \cdot 2 = \frac{x}{2} \cdot 2$

Step 2.1.1.3

Multiply $- \frac{x}{3} \cdot 2$ .

Tap for more steps...

Step 2.1.1.3.1

Multiply $2$ by $- 1$ .

$40 - 2 \frac{x}{3} = \frac{x}{2} \cdot 2$

Step 2.1.1.3.2

Combine $- 2$ and $\frac{x}{3}$ .

$40 + \frac{- 2 x}{3} = \frac{x}{2} \cdot 2$

Step 2.1.1.4

Move the negative in front of the fraction.

$40 - \frac{2 x}{3} = \frac{x}{2} \cdot 2$

Step 2.1.1.5

Reorder $40$ and $- \frac{2 x}{3}$ .

$- \frac{2 x}{3} + 40 = \frac{x}{2} \cdot 2$

Step 2.2

Simplify the right side.

Tap for more steps...

Step 2.2.1

Cancel the common factor of $2$ .

Tap for more steps...

Step 2.2.1.1

Cancel the common factor.

$- \frac{2 x}{3} + 40 = \frac{x}{2} \cdot 2$

Step 2.2.1.2

Rewrite the expression.

$- \frac{2 x}{3} + 40 = x$

Step 3

Solve for $x$ .

Tap for more steps...

Step 3.1

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

Tap for more steps...

Step 3.1.1

Subtract $x$ from both sides of the equation.

$- \frac{2 x}{3} + 40 - x = 0$

Step 3.1.2

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

$- \frac{2 x}{3} - x \cdot \frac{3}{3} + 40 = 0$

Step 3.1.3

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

$- \frac{2 x}{3} + \frac{- x \cdot 3}{3} + 40 = 0$

Step 3.1.4

Combine the numerators over the common denominator.

$\frac{- 2 x - x \cdot 3}{3} + 40 = 0$

Step 3.1.5

Simplify each term.

Tap for more steps...

Step 3.1.5.1

Simplify the numerator.

Tap for more steps...

Step 3.1.5.1.1

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

Tap for more steps...

Step 3.1.5.1.1.1

Factor $x$ out of $- 2 x$ .

$\frac{x \cdot - 2 - x \cdot 3}{3} + 40 = 0$

Step 3.1.5.1.1.2

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

$\frac{x \cdot - 2 + x (- 1 \cdot 3)}{3} + 40 = 0$

Step 3.1.5.1.1.3

Factor $x$ out of $x \cdot - 2 + x (- 1 \cdot 3)$ .

$\frac{x (- 2 - 1 \cdot 3)}{3} + 40 = 0$

Step 3.1.5.1.2

Multiply $- 1$ by $3$ .

$\frac{x (- 2 - 3)}{3} + 40 = 0$

Step 3.1.5.1.3

Subtract $3$ from $- 2$ .

$\frac{x \cdot - 5}{3} + 40 = 0$

Step 3.1.5.2

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

$\frac{- 5 \cdot x}{3} + 40 = 0$

Step 3.1.5.3

Move the negative in front of the fraction.

$- \frac{5 x}{3} + 40 = 0$

Step 3.2

Subtract $40$ from both sides of the equation.

$- \frac{5 x}{3} = - 40$

Step 3.3

Multiply both sides of the equation by $- \frac{3}{5}$ .

$- \frac{3}{5} (- \frac{5 x}{3}) = - \frac{3}{5} \cdot - 40$

Step 3.4

Simplify both sides of the equation.

Tap for more steps...

Step 3.4.1

Simplify the left side.

Tap for more steps...

Step 3.4.1.1

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

Tap for more steps...

Step 3.4.1.1.1

Cancel the common factor of $3$ .

Tap for more steps...

Step 3.4.1.1.1.1

Move the leading negative in $- \frac{3}{5}$ into the numerator.

$\frac{- 3}{5} (- \frac{5 x}{3}) = - \frac{3}{5} \cdot - 40$

Step 3.4.1.1.1.2

Move the leading negative in $- \frac{5 x}{3}$ into the numerator.

$\frac{- 3}{5} \cdot \frac{- 5 x}{3} = - \frac{3}{5} \cdot - 40$

Step 3.4.1.1.1.3

Factor $3$ out of $- 3$ .

$\frac{3 (- 1)}{5} \cdot \frac{- 5 x}{3} = - \frac{3}{5} \cdot - 40$

Step 3.4.1.1.1.4

Cancel the common factor.

$\frac{3 \cdot - 1}{5} \cdot \frac{- 5 x}{3} = - \frac{3}{5} \cdot - 40$

Step 3.4.1.1.1.5

Rewrite the expression.

$\frac{- 1}{5} (- 5 x) = - \frac{3}{5} \cdot - 40$

Step 3.4.1.1.2

Cancel the common factor of $5$ .

Tap for more steps...

Step 3.4.1.1.2.1

Factor $5$ out of $- 5 x$ .

$\frac{- 1}{5} (5 (- x)) = - \frac{3}{5} \cdot - 40$

Step 3.4.1.1.2.2

Cancel the common factor.

$\frac{- 1}{5} (5 (- x)) = - \frac{3}{5} \cdot - 40$

Step 3.4.1.1.2.3

Rewrite the expression.

$- - x = - \frac{3}{5} \cdot - 40$

Step 3.4.1.1.3

Multiply.

Tap for more steps...

Step 3.4.1.1.3.1

Multiply $- 1$ by $- 1$ .

$1 x = - \frac{3}{5} \cdot - 40$

Step 3.4.1.1.3.2

Multiply $x$ by $1$ .

$x = - \frac{3}{5} \cdot - 40$

Step 3.4.2

Simplify the right side.

Tap for more steps...

Step 3.4.2.1

Simplify $- \frac{3}{5} \cdot - 40$ .

Tap for more steps...

Step 3.4.2.1.1

Cancel the common factor of $5$ .

Tap for more steps...

Step 3.4.2.1.1.1

Move the leading negative in $- \frac{3}{5}$ into the numerator.

$x = \frac{- 3}{5} \cdot - 40$

Step 3.4.2.1.1.2

Factor $5$ out of $- 40$ .

$x = \frac{- 3}{5} \cdot (5 (- 8))$

Step 3.4.2.1.1.3

Cancel the common factor.

$x = \frac{- 3}{5} \cdot (5 \cdot - 8)$

Step 3.4.2.1.1.4

Rewrite the expression.

$x = - 3 \cdot - 8$

Step 3.4.2.1.2

Multiply $- 3$ by $- 8$ .

$x = 24$