Algebra Examples

$\frac{x}{5} - \frac{2}{9} = \frac{x}{15}$

Step 1

Multiply both sides by $15$ .

$(\frac{x}{5} - \frac{2}{9}) \cdot 15 = \frac{x}{15} \cdot 15$

Step 2

Simplify.

Tap for more steps...

Step 2.1

Simplify the left side.

Tap for more steps...

Step 2.1.1

Simplify $(\frac{x}{5} - \frac{2}{9}) \cdot 15$ .

Tap for more steps...

Step 2.1.1.1

Simplify terms.

Tap for more steps...

Step 2.1.1.1.1

Apply the distributive property.

$\frac{x}{5} \cdot 15 - \frac{2}{9} \cdot 15 = \frac{x}{15} \cdot 15$

Step 2.1.1.1.2

Cancel the common factor of $5$ .

Tap for more steps...

Step 2.1.1.1.2.1

Factor $5$ out of $15$ .

$\frac{x}{5} \cdot (5 (3)) - \frac{2}{9} \cdot 15 = \frac{x}{15} \cdot 15$

Step 2.1.1.1.2.2

Cancel the common factor.

$\frac{x}{5} \cdot (5 \cdot 3) - \frac{2}{9} \cdot 15 = \frac{x}{15} \cdot 15$

Step 2.1.1.1.2.3

Rewrite the expression.

$x \cdot 3 - \frac{2}{9} \cdot 15 = \frac{x}{15} \cdot 15$

Step 2.1.1.1.3

Cancel the common factor of $3$ .

Tap for more steps...

Step 2.1.1.1.3.1

Move the leading negative in $- \frac{2}{9}$ into the numerator.

$x \cdot 3 + \frac{- 2}{9} \cdot 15 = \frac{x}{15} \cdot 15$

Step 2.1.1.1.3.2

Factor $3$ out of $9$ .

$x \cdot 3 + \frac{- 2}{3 (3)} \cdot 15 = \frac{x}{15} \cdot 15$

Step 2.1.1.1.3.3

Factor $3$ out of $15$ .

$x \cdot 3 + \frac{- 2}{3 \cdot 3} \cdot (3 \cdot 5) = \frac{x}{15} \cdot 15$

Step 2.1.1.1.3.4

Cancel the common factor.

$x \cdot 3 + \frac{- 2}{3 \cdot 3} \cdot (3 \cdot 5) = \frac{x}{15} \cdot 15$

Step 2.1.1.1.3.5

Rewrite the expression.

$x \cdot 3 + \frac{- 2}{3} \cdot 5 = \frac{x}{15} \cdot 15$

Step 2.1.1.1.4

Combine $\frac{- 2}{3}$ and $5$ .

$x \cdot 3 + \frac{- 2 \cdot 5}{3} = \frac{x}{15} \cdot 15$

Step 2.1.1.1.5

Multiply $- 2$ by $5$ .

$x \cdot 3 + \frac{- 10}{3} = \frac{x}{15} \cdot 15$

Step 2.1.1.2

Simplify each term.

Tap for more steps...

Step 2.1.1.2.1

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

$3 \cdot x + \frac{- 10}{3} = \frac{x}{15} \cdot 15$

Step 2.1.1.2.2

Move the negative in front of the fraction.

$3 x - \frac{10}{3} = \frac{x}{15} \cdot 15$

Step 2.2

Simplify the right side.

Tap for more steps...

Step 2.2.1

Cancel the common factor of $15$ .

Tap for more steps...

Step 2.2.1.1

Cancel the common factor.

$3 x - \frac{10}{3} = \frac{x}{15} \cdot 15$

Step 2.2.1.2

Rewrite the expression.

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

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.

$3 x - \frac{10}{3} - x = 0$

Step 3.1.2

Subtract $x$ from $3 x$ .

$2 x - \frac{10}{3} = 0$

Step 3.2

Add $\frac{10}{3}$ to both sides of the equation.

$2 x = \frac{10}{3}$

Step 3.3

Divide each term in $2 x = \frac{10}{3}$ by $2$ and simplify.

Tap for more steps...

Step 3.3.1

Divide each term in $2 x = \frac{10}{3}$ by $2$ .

$\frac{2 x}{2} = \frac{\frac{10}{3}}{2}$

Step 3.3.2

Simplify the left side.

Tap for more steps...

Step 3.3.2.1

Cancel the common factor of $2$ .

Tap for more steps...

Step 3.3.2.1.1

Cancel the common factor.

$\frac{2 x}{2} = \frac{\frac{10}{3}}{2}$

Step 3.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{\frac{10}{3}}{2}$

Step 3.3.3

Simplify the right side.

Tap for more steps...

Step 3.3.3.1

Multiply the numerator by the reciprocal of the denominator.

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

Step 3.3.3.2

Cancel the common factor of $2$ .

Tap for more steps...

Step 3.3.3.2.1

Factor $2$ out of $10$ .

$x = \frac{2 (5)}{3} \cdot \frac{1}{2}$

Step 3.3.3.2.2

Cancel the common factor.

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

Step 3.3.3.2.3

Rewrite the expression.

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

Step 4

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = 1.\overline{6}$

Mixed Number Form:

$x = 1 \frac{2}{3}$