Pre-Algebra Examples

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

Step 1

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

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

Step 2

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

Tap for more steps...

Step 2.1

Combine the numerators over the common denominator.

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

Step 2.2

Add $2$ and $2$ .

$\frac{2 x}{3} + \frac{1}{3} = - \frac{1}{3} x + \frac{4}{5}$

Step 2.3

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

$\frac{2 x}{3} + \frac{1}{3} = - \frac{x}{3} + \frac{4}{5}$

Step 3

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

Tap for more steps...

Step 3.1

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

$\frac{2 x}{3} + \frac{1}{3} + \frac{x}{3} = \frac{4}{5}$

Step 3.2

Combine the numerators over the common denominator.

$\frac{2 x + 1 + x}{3} = \frac{4}{5}$

Step 3.3

Add $2 x$ and $x$ .

$\frac{3 x + 1}{3} = \frac{4}{5}$

Step 4

Multiply both sides by $3$ .

$\frac{3 x + 1}{3} \cdot 3 = \frac{4}{5} \cdot 3$

Step 5

Simplify.

Tap for more steps...

Step 5.1

Simplify the left side.

Tap for more steps...

Step 5.1.1

Cancel the common factor of $3$ .

Tap for more steps...

Step 5.1.1.1

Cancel the common factor.

$\frac{3 x + 1}{3} \cdot 3 = \frac{4}{5} \cdot 3$

Step 5.1.1.2

Rewrite the expression.

$3 x + 1 = \frac{4}{5} \cdot 3$

Step 5.2

Simplify the right side.

Tap for more steps...

Step 5.2.1

Multiply $\frac{4}{5} \cdot 3$ .

Tap for more steps...

Step 5.2.1.1

Combine $\frac{4}{5}$ and $3$ .

$3 x + 1 = \frac{4 \cdot 3}{5}$

Step 5.2.1.2

Multiply $4$ by $3$ .

$3 x + 1 = \frac{12}{5}$

Step 6

Solve for $x$ .

Tap for more steps...

Step 6.1

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

Tap for more steps...

Step 6.1.1

Subtract $1$ from both sides of the equation.

$3 x = \frac{12}{5} - 1$

Step 6.1.2

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$3 x = \frac{12}{5} - 1 \cdot \frac{5}{5}$

Step 6.1.3

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

$3 x = \frac{12}{5} + \frac{- 1 \cdot 5}{5}$

Step 6.1.4

Combine the numerators over the common denominator.

$3 x = \frac{12 - 1 \cdot 5}{5}$

Step 6.1.5

Simplify the numerator.

Tap for more steps...

Step 6.1.5.1

Multiply $- 1$ by $5$ .

$3 x = \frac{12 - 5}{5}$

Step 6.1.5.2

Subtract $5$ from $12$ .

$3 x = \frac{7}{5}$

Step 6.2

Divide each term in $3 x = \frac{7}{5}$ by $3$ and simplify.

Tap for more steps...

Step 6.2.1

Divide each term in $3 x = \frac{7}{5}$ by $3$ .

$\frac{3 x}{3} = \frac{\frac{7}{5}}{3}$

Step 6.2.2

Simplify the left side.

Tap for more steps...

Step 6.2.2.1

Cancel the common factor of $3$ .

Tap for more steps...

Step 6.2.2.1.1

Cancel the common factor.

$\frac{3 x}{3} = \frac{\frac{7}{5}}{3}$

Step 6.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{\frac{7}{5}}{3}$

Step 6.2.3

Simplify the right side.

Tap for more steps...

Step 6.2.3.1

Multiply the numerator by the reciprocal of the denominator.

$x = \frac{7}{5} \cdot \frac{1}{3}$

Step 6.2.3.2

Multiply $\frac{7}{5} \cdot \frac{1}{3}$ .

Tap for more steps...

Step 6.2.3.2.1

Multiply $\frac{7}{5}$ by $\frac{1}{3}$ .

$x = \frac{7}{5 \cdot 3}$

Step 6.2.3.2.2

Multiply $5$ by $3$ .

$x = \frac{7}{15}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$x = \frac{7}{15}$

Decimal Form:

$x = 0.4\overline{6}$