Finite Math Examples

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

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

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

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

Step 1.2

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

$\frac{5 x}{4} - \frac{y \cdot 2}{3} = 3$

Step 1.3

Move $2$ to the left of $y$ .

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

Step 2

Add $\frac{2 y}{3}$ to both sides of the equation.

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

Step 3

Multiply both sides of the equation by $\frac{4}{5}$ .

$\frac{4}{5} \cdot \frac{5 x}{4} = \frac{4}{5} (3 + \frac{2 y}{3})$

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 $\frac{4}{5} \cdot \frac{5 x}{4}$ .

Tap for more steps...

Step 4.1.1.1

Cancel the common factor of $4$ .

Tap for more steps...

Step 4.1.1.1.1

Cancel the common factor.

$\frac{4}{5} \cdot \frac{5 x}{4} = \frac{4}{5} (3 + \frac{2 y}{3})$

Step 4.1.1.1.2

Rewrite the expression.

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

Step 4.1.1.2

Cancel the common factor of $5$ .

Tap for more steps...

Step 4.1.1.2.1

Factor $5$ out of $5 x$ .

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

Step 4.1.1.2.2

Cancel the common factor.

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

Step 4.1.1.2.3

Rewrite the expression.

$x = \frac{4}{5} (3 + \frac{2 y}{3})$

Step 4.2

Simplify the right side.

Tap for more steps...

Step 4.2.1

Simplify $\frac{4}{5} (3 + \frac{2 y}{3})$ .

Tap for more steps...

Step 4.2.1.1

Apply the distributive property.

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

Step 4.2.1.2

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

Tap for more steps...

Step 4.2.1.2.1

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

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

Step 4.2.1.2.2

Multiply $4$ by $3$ .

$x = \frac{12}{5} + \frac{4}{5} \cdot \frac{2 y}{3}$

Step 4.2.1.3

Multiply $\frac{4}{5} \cdot \frac{2 y}{3}$ .

Tap for more steps...

Step 4.2.1.3.1

Multiply $\frac{4}{5}$ by $\frac{2 y}{3}$ .

$x = \frac{12}{5} + \frac{4 (2 y)}{5 \cdot 3}$

Step 4.2.1.3.2

Multiply $2$ by $4$ .

$x = \frac{12}{5} + \frac{8 y}{5 \cdot 3}$

Step 4.2.1.3.3

Multiply $5$ by $3$ .

$x = \frac{12}{5} + \frac{8 y}{15}$

Step 5

Reorder $\frac{12}{5}$ and $\frac{8 y}{15}$ .

$x = \frac{8 y}{15} + \frac{12}{5}$