Pre-Algebra Examples

$y + 9 = \frac{3}{2} \cdot (x - 5)$

Step 1

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

Step 2

Multiply both sides by $2$ .

$2 (y + 9) = 2 (\frac{3}{2} \cdot (x - 5))$

Step 3

Simplify the left side.

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Step 3.1

Simplify $2 (y + 9)$ .

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Step 3.1.1

Apply the distributive property.

$2 y + 2 \cdot 9 = 2 (\frac{3}{2} \cdot (x - 5))$

Step 3.1.2

Multiply $2$ by $9$ .

$2 y + 18 = 2 (\frac{3}{2} \cdot (x - 5))$

Step 4

Simplify the right side.

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Step 4.1

Simplify $2 (\frac{3}{2} \cdot (x - 5))$ .

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Step 4.1.1

Apply the distributive property.

$2 y + 18 = 2 (\frac{3}{2} x + \frac{3}{2} \cdot - 5)$

Step 4.1.2

Combine $\frac{3}{2}$ and $x$ .

$2 y + 18 = 2 (\frac{3 x}{2} + \frac{3}{2} \cdot - 5)$

Step 4.1.3

Multiply $\frac{3}{2} \cdot - 5$ .

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Step 4.1.3.1

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

$2 y + 18 = 2 (\frac{3 x}{2} + \frac{3 \cdot - 5}{2})$

Step 4.1.3.2

Multiply $3$ by $- 5$ .

$2 y + 18 = 2 (\frac{3 x}{2} + \frac{- 15}{2})$

Step 4.1.4

Move the negative in front of the fraction.

$2 y + 18 = 2 (\frac{3 x}{2} - \frac{15}{2})$

Step 4.1.5

Apply the distributive property.

$2 y + 18 = 2 \frac{3 x}{2} + 2 (- \frac{15}{2})$

Step 4.1.6

Cancel the common factor of $2$ .

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Step 4.1.6.1

Cancel the common factor.

$2 y + 18 = 2 \frac{3 x}{2} + 2 (- \frac{15}{2})$

Step 4.1.6.2

Rewrite the expression.

$2 y + 18 = 3 x + 2 (- \frac{15}{2})$

Step 4.1.7

Cancel the common factor of $2$ .

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Step 4.1.7.1

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

$2 y + 18 = 3 x + 2 (\frac{- 15}{2})$

Step 4.1.7.2

Cancel the common factor.

$2 y + 18 = 3 x + 2 (\frac{- 15}{2})$

Step 4.1.7.3

Rewrite the expression.

$2 y + 18 = 3 x - 15$

Step 5

Rewrite the equation.

$3 x - 15 = 2 y + 18$

Step 6

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

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Step 6.1

Subtract $2 y$ from both sides of the equation.

$3 x - 15 - 2 y = 18$

Step 6.2

Move $- 15$ .

$3 x - 2 y - 15 = 18$

Step 7

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

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Step 7.1

Add $15$ to both sides of the equation.

$3 x - 2 y = 18 + 15$

Step 7.2

Add $18$ and $15$ .

$3 x - 2 y = 33$

Step 8