Pre-Algebra Examples

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

Step 1

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

Step 2

Multiply both sides by $2$ .

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

Step 3

Simplify the left side.

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Step 3.1

Simplify $2 (y - 2)$ .

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Step 3.1.1

Apply the distributive property.

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

Step 3.1.2

Multiply $2$ by $- 2$ .

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

Step 4

Simplify the right side.

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Step 4.1

Simplify $2 (- \frac{5}{2} \cdot (x + 6))$ .

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Step 4.1.1

Simplify terms.

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Step 4.1.1.1

Apply the distributive property.

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

Step 4.1.1.2

Combine $x$ and $\frac{5}{2}$ .

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

Step 4.1.1.3

Cancel the common factor of $2$ .

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Step 4.1.1.3.1

Move the leading negative in $- \frac{5}{2}$ into the numerator.

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

Step 4.1.1.3.2

Factor $2$ out of $6$ .

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

Step 4.1.1.3.3

Cancel the common factor.

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

Step 4.1.1.3.4

Rewrite the expression.

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

Step 4.1.1.4

Multiply $- 5$ by $3$ .

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

Step 4.1.2

Move $5$ to the left of $x$ .

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

Step 4.1.3

Simplify terms.

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Step 4.1.3.1

Apply the distributive property.

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

Step 4.1.3.2

Cancel the common factor of $2$ .

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Step 4.1.3.2.1

Move the leading negative in $- \frac{5 x}{2}$ into the numerator.

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

Step 4.1.3.2.2

Cancel the common factor.

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

Step 4.1.3.2.3

Rewrite the expression.

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

Step 4.1.3.3

Multiply $2$ by $- 15$ .

$2 y - 4 = - 5 x - 30$

Step 5

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

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Step 5.1

Add $5 x$ to both sides of the equation.

$2 y - 4 + 5 x = - 30$

Step 5.2

Move $- 4$ .

$2 y + 5 x - 4 = - 30$

Step 5.3

Reorder $2 y$ and $5 x$ .

$5 x + 2 y - 4 = - 30$

Step 6

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

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Step 6.1

Add $4$ to both sides of the equation.

$5 x + 2 y = - 30 + 4$

Step 6.2

Add $- 30$ and $4$ .

$5 x + 2 y = - 26$

Step 7