Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

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

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

Step 1.2

Combine $\frac{1}{4}$ and $y$ .

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

Step 2

Subtract $\frac{3 x}{4}$ from both sides of the equation.

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

Step 3

Multiply both sides of the equation by $4$ .

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

Step 4

Simplify both sides of the equation.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Cancel the common factor of $4$ .

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Step 4.1.1.1

Cancel the common factor.

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

Step 4.1.1.2

Rewrite the expression.

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

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $4 (5 - \frac{3 x}{4})$ .

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Step 4.2.1.1

Apply the distributive property.

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

Step 4.2.1.2

Multiply $4$ by $5$ .

$y = 20 + 4 (- \frac{3 x}{4})$

Step 4.2.1.3

Cancel the common factor of $4$ .

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Step 4.2.1.3.1

Move the leading negative in $- \frac{3 x}{4}$ into the numerator.

$y = 20 + 4 \frac{- 3 x}{4}$

Step 4.2.1.3.2

Cancel the common factor.

$y = 20 + 4 \frac{- 3 x}{4}$

Step 4.2.1.3.3

Rewrite the expression.

$y = 20 - 3 x$

Step 5

Reorder $20$ and $- 3 x$ .

$y = - 3 x + 20$