Pre-Algebra Examples

$y - 3 = \frac{1}{2} \cdot (x - 3)$

Step 1

Simplify $\frac{1}{2} \cdot (x - 3)$ .

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Step 1.1

Rewrite.

$y - 3 = 0 + 0 + \frac{1}{2} \cdot (x - 3)$

Step 1.2

Simplify by adding zeros.

$y - 3 = \frac{1}{2} \cdot (x - 3)$

Step 1.3

Apply the distributive property.

$y - 3 = \frac{1}{2} x + \frac{1}{2} \cdot - 3$

Step 1.4

Combine $\frac{1}{2}$ and $x$ .

$y - 3 = \frac{x}{2} + \frac{1}{2} \cdot - 3$

Step 1.5

Combine $\frac{1}{2}$ and $- 3$ .

$y - 3 = \frac{x}{2} + \frac{- 3}{2}$

Step 1.6

Move the negative in front of the fraction.

$y - 3 = \frac{x}{2} - \frac{3}{2}$

Step 2

Move all terms not containing $y$ to the right side of the equation.

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Step 2.1

Add $3$ to both sides of the equation.

$y = \frac{x}{2} - \frac{3}{2} + 3$

Step 2.2

To write $3$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$y = \frac{x}{2} - \frac{3}{2} + 3 \cdot \frac{2}{2}$

Step 2.3

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

$y = \frac{x}{2} - \frac{3}{2} + \frac{3 \cdot 2}{2}$

Step 2.4

Combine the numerators over the common denominator.

$y = \frac{x}{2} + \frac{- 3 + 3 \cdot 2}{2}$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $3$ by $2$ .

$y = \frac{x}{2} + \frac{- 3 + 6}{2}$

Step 2.5.2

Add $- 3$ and $6$ .

$y = \frac{x}{2} + \frac{3}{2}$