Pre-Algebra Examples

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

Step 1

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

Step 2

Multiply both sides by $4$ .

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

Step 3

Simplify the left side.

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Step 3.1

Simplify $4 (y - 5)$ .

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Step 3.1.1

Apply the distributive property.

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

Step 3.1.2

Multiply $4$ by $- 5$ .

$4 y - 20 = 4 (- \frac{1}{4} \cdot (x + 3))$

Step 4

Simplify the right side.

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Step 4.1

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

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Step 4.1.1

Apply the distributive property.

$4 y - 20 = 4 (- \frac{1}{4} x - \frac{1}{4} \cdot 3)$

Step 4.1.2

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

$4 y - 20 = 4 (- \frac{x}{4} - \frac{1}{4} \cdot 3)$

Step 4.1.3

Multiply $- \frac{1}{4} \cdot 3$ .

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Step 4.1.3.1

Multiply $3$ by $- 1$ .

$4 y - 20 = 4 (- \frac{x}{4} - 3 (\frac{1}{4}))$

Step 4.1.3.2

Combine $- 3$ and $\frac{1}{4}$ .

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

Step 4.1.4

Move the negative in front of the fraction.

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

Step 4.1.5

Apply the distributive property.

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

Step 4.1.6

Cancel the common factor of $4$ .

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Step 4.1.6.1

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

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

Step 4.1.6.2

Cancel the common factor.

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

Step 4.1.6.3

Rewrite the expression.

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

Step 4.1.7

Cancel the common factor of $4$ .

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Step 4.1.7.1

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

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

Step 4.1.7.2

Cancel the common factor.

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

Step 4.1.7.3

Rewrite the expression.

$4 y - 20 = - x - 3$

Step 5

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

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Step 5.1

Add $x$ to both sides of the equation.

$4 y - 20 + x = - 3$

Step 5.2

Move $- 20$ .

$4 y + x - 20 = - 3$

Step 5.3

Reorder $4 y$ and $x$ .

$x + 4 y - 20 = - 3$

Step 6

Move all terms not containing a variable to the right side of the equation.

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Step 6.1

Add $20$ to both sides of the equation.

$x + 4 y = - 3 + 20$

Step 6.2

Add $- 3$ and $20$ .

$x + 4 y = 17$

Step 7