Pre-Algebra Examples

$y + 4 = \frac{5}{4} \cdot (x - 6)$

Step 1

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

Step 2

Multiply both sides by $4$ .

$4 (y + 4) = 4 (\frac{5}{4} \cdot (x - 6))$

Step 3

Simplify the left side.

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Step 3.1

Simplify $4 (y + 4)$ .

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Step 3.1.1

Apply the distributive property.

$4 y + 4 \cdot 4 = 4 (\frac{5}{4} \cdot (x - 6))$

Step 3.1.2

Multiply $4$ by $4$ .

$4 y + 16 = 4 (\frac{5}{4} \cdot (x - 6))$

Step 4

Simplify the right side.

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Step 4.1

Simplify $4 (\frac{5}{4} \cdot (x - 6))$ .

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Step 4.1.1

Apply the distributive property.

$4 y + 16 = 4 (\frac{5}{4} x + \frac{5}{4} \cdot - 6)$

Step 4.1.2

Combine $\frac{5}{4}$ and $x$ .

$4 y + 16 = 4 (\frac{5 x}{4} + \frac{5}{4} \cdot - 6)$

Step 4.1.3

Cancel the common factor of $2$ .

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Step 4.1.3.1

Factor $2$ out of $4$ .

$4 y + 16 = 4 (\frac{5 x}{4} + \frac{5}{2 (2)} \cdot - 6)$

Step 4.1.3.2

Factor $2$ out of $- 6$ .

$4 y + 16 = 4 (\frac{5 x}{4} + \frac{5}{2 \cdot 2} \cdot (2 \cdot - 3))$

Step 4.1.3.3

Cancel the common factor.

$4 y + 16 = 4 (\frac{5 x}{4} + \frac{5}{2 \cdot 2} \cdot (2 \cdot - 3))$

Step 4.1.3.4

Rewrite the expression.

$4 y + 16 = 4 (\frac{5 x}{4} + \frac{5}{2} \cdot - 3)$

Step 4.1.4

Combine $\frac{5}{2}$ and $- 3$ .

$4 y + 16 = 4 (\frac{5 x}{4} + \frac{5 \cdot - 3}{2})$

Step 4.1.5

Simplify the expression.

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Step 4.1.5.1

Multiply $5$ by $- 3$ .

$4 y + 16 = 4 (\frac{5 x}{4} + \frac{- 15}{2})$

Step 4.1.5.2

Move the negative in front of the fraction.

$4 y + 16 = 4 (\frac{5 x}{4} - \frac{15}{2})$

Step 4.1.6

Apply the distributive property.

$4 y + 16 = 4 \frac{5 x}{4} + 4 (- \frac{15}{2})$

Step 4.1.7

Cancel the common factor of $4$ .

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Step 4.1.7.1

Cancel the common factor.

$4 y + 16 = 4 \frac{5 x}{4} + 4 (- \frac{15}{2})$

Step 4.1.7.2

Rewrite the expression.

$4 y + 16 = 5 x + 4 (- \frac{15}{2})$

Step 4.1.8

Cancel the common factor of $2$ .

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Step 4.1.8.1

Move the leading negative in $- \frac{15}{2}$ into the numerator.

$4 y + 16 = 5 x + 4 (\frac{- 15}{2})$

Step 4.1.8.2

Factor $2$ out of $4$ .

$4 y + 16 = 5 x + 2 (2) \frac{- 15}{2}$

Step 4.1.8.3

Cancel the common factor.

$4 y + 16 = 5 x + 2 \cdot 2 \frac{- 15}{2}$

Step 4.1.8.4

Rewrite the expression.

$4 y + 16 = 5 x + 2 \cdot - 15$

Step 4.1.9

Multiply $2$ by $- 15$ .

$4 y + 16 = 5 x - 30$

Step 5

Rewrite the equation.

$5 x - 30 = 4 y + 16$

Step 6

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

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Step 6.1

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

$5 x - 30 - 4 y = 16$

Step 6.2

Move $- 30$ .

$5 x - 4 y - 30 = 16$

Step 7

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

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Step 7.1

Add $30$ to both sides of the equation.

$5 x - 4 y = 16 + 30$

Step 7.2

Add $16$ and $30$ .

$5 x - 4 y = 46$

Step 8