Algebra Examples

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

Step 1

Solve the equation for $y$ .

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Step 1.1

Subtract $\frac{x}{4}$ from both sides of the equation.

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

Step 1.2

Multiply both sides of the equation by $- 3$ .

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

Step 1.3

Simplify both sides of the equation.

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Step 1.3.1

Simplify the left side.

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Step 1.3.1.1

Simplify $- 3 (- \frac{y}{3})$ .

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Step 1.3.1.1.1

Cancel the common factor of $3$ .

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Step 1.3.1.1.1.1

Move the leading negative in $- \frac{y}{3}$ into the numerator.

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

Step 1.3.1.1.1.2

Factor $3$ out of $- 3$ .

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

Step 1.3.1.1.1.3

Cancel the common factor.

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

Step 1.3.1.1.1.4

Rewrite the expression.

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

Step 1.3.1.1.2

Multiply.

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Step 1.3.1.1.2.1

Multiply $- 1$ by $- 1$ .

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

Step 1.3.1.1.2.2

Multiply $y$ by $1$ .

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

Step 1.3.2

Simplify the right side.

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Step 1.3.2.1

Simplify $- 3 (1 - \frac{x}{4})$ .

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Step 1.3.2.1.1

Apply the distributive property.

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

Step 1.3.2.1.2

Multiply $- 3$ by $1$ .

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

Step 1.3.2.1.3

Multiply $- 3 (- \frac{x}{4})$ .

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Step 1.3.2.1.3.1

Multiply $- 1$ by $- 3$ .

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

Step 1.3.2.1.3.2

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

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

Step 1.4

Reorder $- 3$ and $\frac{3 x}{4}$ .

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

Step 2

A linear equation is an equation of a straight line, which means that the degree of a linear equation must be $0$ or $1$ for each of its variables. In this case, the degree of variable $y$ is $1$ and the degree of variable $x$ is $1$ .

Linear