Pre-Algebra Examples

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

Step 1

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

Step 2

Multiply both sides by $2$ .

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

Step 3

Simplify the left side.

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Step 3.1

Simplify $2 (y - 1)$ .

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Step 3.1.1

Apply the distributive property.

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

Step 3.1.2

Multiply $2$ by $- 1$ .

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

Step 4

Simplify the right side.

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Step 4.1

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

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Step 4.1.1

Apply the distributive property.

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

Step 4.1.2

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

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

Step 4.1.3

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

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

Step 4.1.4

Move the negative in front of the fraction.

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

Step 4.1.5

Apply the distributive property.

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

Step 4.1.6

Cancel the common factor of $2$ .

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Step 4.1.6.1

Cancel the common factor.

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

Step 4.1.6.2

Rewrite the expression.

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

Step 4.1.7

Cancel the common factor of $2$ .

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Step 4.1.7.1

Move the leading negative in $- \frac{3}{2}$ into the numerator.

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

Step 4.1.7.2

Cancel the common factor.

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

Step 4.1.7.3

Rewrite the expression.

$2 y - 2 = x - 3$

Step 5

Rewrite the equation.

$x - 3 = 2 y - 2$

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.

$x - 3 - 2 y = - 2$

Step 6.2

Move $- 3$ .

$x - 2 y - 3 = - 2$

Step 7

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

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Step 7.1

Add $3$ to both sides of the equation.

$x - 2 y = - 2 + 3$

Step 7.2

Add $- 2$ and $3$ .

$x - 2 y = 1$

Step 8