Algebra Examples

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

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.

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Step 2.1

Multiply both sides by $2$ .

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

Step 2.2

Simplify.

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Step 2.2.1

Simplify the left side.

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Step 2.2.1.1

Cancel the common factor of $2$ .

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Step 2.2.1.1.1

Cancel the common factor.

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

Step 2.2.1.1.2

Rewrite the expression.

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

Step 2.2.2

Simplify the right side.

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Step 2.2.2.1

Cancel the common factor of $2$ .

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Step 2.2.2.1.1

Factor $2$ out of $4$ .

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

Step 2.2.2.1.2

Cancel the common factor.

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

Step 2.2.2.1.3

Rewrite the expression.

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

Step 2.3

Solve for $y$ .

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Step 2.3.1

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

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Step 2.3.1.1

Split the fraction $\frac{5 x - 3}{2}$ into two fractions.

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

Step 2.3.1.2

Move the negative in front of the fraction.

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

Step 2.3.2

Subtract $4 x$ from both sides of the equation.

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

Step 2.3.3

Divide each term in $- y = \frac{5 x}{2} - \frac{3}{2} - 4 x$ by $- 1$ and simplify.

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Step 2.3.3.1

Divide each term in $- y = \frac{5 x}{2} - \frac{3}{2} - 4 x$ by $- 1$ .

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

Step 2.3.3.2

Simplify the left side.

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Step 2.3.3.2.1

Dividing two negative values results in a positive value.

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

Step 2.3.3.2.2

Divide $y$ by $1$ .

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

Step 2.3.3.3

Simplify the right side.

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Step 2.3.3.3.1

Simplify each term.

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Step 2.3.3.3.1.1

Move the negative one from the denominator of $\frac{\frac{5 x}{2}}{- 1}$ .

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

Step 2.3.3.3.1.2

Rewrite $- 1 \cdot \frac{5 x}{2}$ as $- \frac{5 x}{2}$ .

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

Step 2.3.3.3.1.3

Dividing two negative values results in a positive value.

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

Step 2.3.3.3.1.4

Divide $\frac{3}{2}$ by $1$ .

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

Step 2.3.3.3.1.5

Move the negative one from the denominator of $\frac{- 4 x}{- 1}$ .

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

Step 2.3.3.3.1.6

Rewrite $- 1 \cdot (- 4 x)$ as $- (- 4 x)$ .

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

Step 2.3.3.3.1.7

Multiply $- 4$ by $- 1$ .

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

Step 2.4

Write in $y = m x + b$ form.

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Step 2.4.1

Simplify $- \frac{5 x}{2} + \frac{3}{2} + 4 x$ .

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Step 2.4.1.1

To write $4 x$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Step 2.4.1.2

Combine $4 x$ and $\frac{2}{2}$ .

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

Step 2.4.1.3

Combine the numerators over the common denominator.

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

Step 2.4.1.4

Combine the numerators over the common denominator.

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

Step 2.4.1.5

Multiply $2$ by $4$ .

$y = \frac{- 5 x + 8 x + 3}{2}$

Step 2.4.1.6

Add $- 5 x$ and $8 x$ .

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

Step 2.4.1.7

Factor $3$ out of $3 x + 3$ .

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Step 2.4.1.7.1

Factor $3$ out of $3 x$ .

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

Step 2.4.1.7.2

Factor $3$ out of $3$ .

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

Step 2.4.1.7.3

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

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

Step 2.4.2

Apply the distributive property.

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

Step 2.4.3

Multiply $3$ by $1$ .

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

Step 2.4.4

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

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

Step 2.4.5

Reorder terms.

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