Algebra Examples

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

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

Step 1

Solve the equation for

y

$y$ .

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Step 1.1

Subtract

\frac{x}{4}

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

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

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

Step 1.2

Multiply both sides of the equation by

- 3

$- 3$ .

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

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

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})

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

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Step 1.3.1.1.1

Cancel the common factor of

3

$3$ .

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Step 1.3.1.1.1.1

Move the leading negative in

- \frac{y}{3}

$- \frac{y}{3}$ into the numerator.

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

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

Step 1.3.1.1.1.2

Factor

3

$3$ out of

- 3

$- 3$ .

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

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

Step 1.3.1.1.1.3

Cancel the common factor.

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

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

Step 1.3.1.1.1.4

Rewrite the expression.

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

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

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

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

Step 1.3.1.1.2

Multiply.

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Step 1.3.1.1.2.1

Multiply

- 1

$- 1$ by

- 1

$- 1$ .

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

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

Step 1.3.1.1.2.2

Multiply

y

$y$ by

1

$1$ .

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

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

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

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

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

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

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

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

Step 1.3.2

Simplify the right side.

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Step 1.3.2.1

Simplify

- 3 (1 - \frac{x}{4})

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

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Step 1.3.2.1.1

Apply the distributive property.

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

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

Step 1.3.2.1.2

Multiply

- 3

$- 3$ by

1

$1$ .

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

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

Step 1.3.2.1.3

Multiply

- 3 (- \frac{x}{4})

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

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Step 1.3.2.1.3.1

Multiply

- 1

$- 1$ by

- 3

$- 3$ .

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

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

Step 1.3.2.1.3.2

Combine

3

$3$ and

\frac{x}{4}

$\frac{x}{4}$ .

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

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

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

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

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

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

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

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

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

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

Step 1.4

Reorder

- 3

$- 3$ and

\frac{3 x}{4}

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

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

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

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

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

Step 2

A linear equation is an equation of a straight line, which means that the degree of a linear equation must be

0

$0$ or

1

$1$ for each of its variables. In this case, the degree of variable

y

$y$ is

1

$1$ and the degree of variable

x

$x$ is

1

$1$ .

Linear