Algebra Examples

$y = \frac{11}{4} x - 2 \frac{5}{8}$

Step 1

The standard form of a linear equation is $A x + B y = C$ .

Step 2

Multiply both sides by $4$ .

$4 y = 4 (\frac{11}{4} x - 2 \frac{5}{8})$

Step 3

Simplify the right side.

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Step 3.1

Simplify $4 (\frac{11}{4} x - 2 \frac{5}{8})$ .

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Step 3.1.1

Convert $2 \frac{5}{8}$ to an improper fraction.

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Step 3.1.1.1

A mixed number is an addition of its whole and fractional parts.

$4 y = 4 (\frac{11}{4} x - (2 + \frac{5}{8}))$

Step 3.1.1.2

Add $2$ and $\frac{5}{8}$ .

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Step 3.1.1.2.1

To write $2$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$4 y = 4 (\frac{11}{4} x - (2 \cdot \frac{8}{8} + \frac{5}{8}))$

Step 3.1.1.2.2

Combine $2$ and $\frac{8}{8}$ .

$4 y = 4 (\frac{11}{4} x - (\frac{2 \cdot 8}{8} + \frac{5}{8}))$

Step 3.1.1.2.3

Combine the numerators over the common denominator.

$4 y = 4 (\frac{11}{4} x - \frac{2 \cdot 8 + 5}{8})$

Step 3.1.1.2.4

Simplify the numerator.

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Step 3.1.1.2.4.1

Multiply $2$ by $8$ .

$4 y = 4 (\frac{11}{4} x - \frac{16 + 5}{8})$

Step 3.1.1.2.4.2

Add $16$ and $5$ .

$4 y = 4 (\frac{11}{4} x - \frac{21}{8})$

Step 3.1.2

Combine $\frac{11}{4}$ and $x$ .

$4 y = 4 (\frac{11 x}{4} - \frac{21}{8})$

Step 3.1.3

Apply the distributive property.

$4 y = 4 \frac{11 x}{4} + 4 (- \frac{21}{8})$

Step 3.1.4

Cancel the common factor of $4$ .

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Step 3.1.4.1

Cancel the common factor.

$4 y = 4 \frac{11 x}{4} + 4 (- \frac{21}{8})$

Step 3.1.4.2

Rewrite the expression.

$4 y = 11 x + 4 (- \frac{21}{8})$

Step 3.1.5

Cancel the common factor of $4$ .

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Step 3.1.5.1

Move the leading negative in $- \frac{21}{8}$ into the numerator.

$4 y = 11 x + 4 (\frac{- 21}{8})$

Step 3.1.5.2

Factor $4$ out of $8$ .

$4 y = 11 x + 4 \frac{- 21}{4 (2)}$

Step 3.1.5.3

Cancel the common factor.

$4 y = 11 x + 4 \frac{- 21}{4 \cdot 2}$

Step 3.1.5.4

Rewrite the expression.

$4 y = 11 x + \frac{- 21}{2}$

Step 3.1.6

Move the negative in front of the fraction.

$4 y = 11 x - \frac{21}{2}$

Step 4

Rewrite the equation.

$11 x - \frac{21}{2} = 4 y$

Step 5

Move all terms containing variables to the left side of the equation.

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Step 5.1

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

$11 x - \frac{21}{2} - 4 y = 0$

Step 5.2

Move $- \frac{21}{2}$ .

$11 x - 4 y - \frac{21}{2} = 0$

Step 6

Add $\frac{21}{2}$ to both sides of the equation.

$11 x - 4 y = \frac{21}{2}$

Step 7