Algebra Examples

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

Step 1

The slope-intercept form is $y = m x + b$ , where $m$ is the slope and $b$ is the y-intercept.

$y = m x + b$

Step 2

Rewrite in slope-intercept form.

Tap for more steps...

Step 2.1

Simplify the right side.

Tap for more steps...

Step 2.1.1

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

Tap for more steps...

Step 2.1.1.1

Factor $3$ out of $3 x$ .

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

Step 2.1.1.2

Factor $3$ out of $- 3$ .

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

Step 2.1.1.3

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

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

Step 2.2

Multiply both sides by $2$ .

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

Step 2.3

Simplify.

Tap for more steps...

Step 2.3.1

Simplify the left side.

Tap for more steps...

Step 2.3.1.1

Cancel the common factor of $2$ .

Tap for more steps...

Step 2.3.1.1.1

Cancel the common factor.

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

Step 2.3.1.1.2

Rewrite the expression.

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

Step 2.3.2

Simplify the right side.

Tap for more steps...

Step 2.3.2.1

Cancel the common factor of $2$ .

Tap for more steps...

Step 2.3.2.1.1

Factor $2$ out of $4$ .

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

Step 2.3.2.1.2

Cancel the common factor.

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

Step 2.3.2.1.3

Rewrite the expression.

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

Step 2.4

Solve for $y$ .

Tap for more steps...

Step 2.4.1

Subtract $5 x$ from both sides of the equation.

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

Step 2.4.2

Divide each term in $- 3 y = \frac{3 (x - 1)}{2} - 5 x$ by $- 3$ and simplify.

Tap for more steps...

Step 2.4.2.1

Divide each term in $- 3 y = \frac{3 (x - 1)}{2} - 5 x$ by $- 3$ .

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

Step 2.4.2.2

Simplify the left side.

Tap for more steps...

Step 2.4.2.2.1

Cancel the common factor of $- 3$ .

Tap for more steps...

Step 2.4.2.2.1.1

Cancel the common factor.

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

Step 2.4.2.2.1.2

Divide $y$ by $1$ .

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

Step 2.4.2.3

Simplify the right side.

Tap for more steps...

Step 2.4.2.3.1

Combine the numerators over the common denominator.

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

Step 2.4.2.3.2

Simplify the numerator.

Tap for more steps...

Step 2.4.2.3.2.1

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

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

Step 2.4.2.3.2.2

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

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

Step 2.4.2.3.2.3

Combine the numerators over the common denominator.

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

Step 2.4.2.3.2.4

Rewrite $\frac{3 (x - 1) - 5 x \cdot 2}{2}$ in a factored form.

Tap for more steps...

Step 2.4.2.3.2.4.1

Apply the distributive property.

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

Step 2.4.2.3.2.4.2

Multiply $3$ by $- 1$ .

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

Step 2.4.2.3.2.4.3

Multiply $2$ by $- 5$ .

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

Step 2.4.2.3.2.4.4

Subtract $10 x$ from $3 x$ .

$y = \frac{\frac{- 7 x - 3}{2}}{- 3}$

Step 2.4.2.3.2.5

Split the fraction $\frac{- 7 x - 3}{2}$ into two fractions.

$y = \frac{\frac{- 7 x}{2} + \frac{- 3}{2}}{- 3}$

Step 2.4.2.3.2.6

Simplify each term.

Tap for more steps...

Step 2.4.2.3.2.6.1

Move the negative in front of the fraction.

$y = \frac{- \frac{7 x}{2} + \frac{- 3}{2}}{- 3}$

Step 2.4.2.3.2.6.2

Move the negative in front of the fraction.

$y = \frac{- \frac{7 x}{2} - \frac{3}{2}}{- 3}$

Step 2.4.2.3.2.7

Factor $- 1$ out of $- \frac{7 x}{2} - \frac{3}{2}$ .

Tap for more steps...

Step 2.4.2.3.2.7.1

Factor $- 1$ out of $- \frac{7 x}{2}$ .

$y = \frac{- (\frac{7 x}{2}) - \frac{3}{2}}{- 3}$

Step 2.4.2.3.2.7.2

Factor $- 1$ out of $- \frac{3}{2}$ .

$y = \frac{- (\frac{7 x}{2}) - (\frac{3}{2})}{- 3}$

Step 2.4.2.3.2.7.3

Factor $- 1$ out of $- (\frac{7 x}{2}) - (\frac{3}{2})$ .

$y = \frac{- (\frac{7 x}{2} + \frac{3}{2})}{- 3}$

Step 2.4.2.3.3

Dividing two negative values results in a positive value.

$y = \frac{\frac{7 x}{2} + \frac{3}{2}}{3}$

Step 2.4.2.3.4

Split the fraction $\frac{\frac{7 x}{2} + \frac{3}{2}}{3}$ into two fractions.

$y = \frac{\frac{7 x}{2}}{3} + \frac{\frac{3}{2}}{3}$

Step 2.4.2.3.5

Simplify each term.

Tap for more steps...

Step 2.4.2.3.5.1

Multiply the numerator by the reciprocal of the denominator.

$y = \frac{7 x}{2} \cdot \frac{1}{3} + \frac{\frac{3}{2}}{3}$

Step 2.4.2.3.5.2

Multiply $\frac{7 x}{2} \cdot \frac{1}{3}$ .

Tap for more steps...

Step 2.4.2.3.5.2.1

Multiply $\frac{7 x}{2}$ by $\frac{1}{3}$ .

$y = \frac{7 x}{2 \cdot 3} + \frac{\frac{3}{2}}{3}$

Step 2.4.2.3.5.2.2

Multiply $2$ by $3$ .

$y = \frac{7 x}{6} + \frac{\frac{3}{2}}{3}$

Step 2.4.2.3.5.3

Multiply the numerator by the reciprocal of the denominator.

$y = \frac{7 x}{6} + \frac{3}{2} \cdot \frac{1}{3}$

Step 2.4.2.3.5.4

Cancel the common factor of $3$ .

Tap for more steps...

Step 2.4.2.3.5.4.1

Cancel the common factor.

$y = \frac{7 x}{6} + \frac{3}{2} \cdot \frac{1}{3}$

Step 2.4.2.3.5.4.2

Rewrite the expression.

$y = \frac{7 x}{6} + \frac{1}{2}$

Step 2.5

Reorder terms.

$y = \frac{7}{6} x + \frac{1}{2}$