Algebra Examples

$y - 1 = \frac{1}{4} (x - 12)$

Step 1

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

Step 2

Multiply both sides by $4$ .

$4 (y - 1) = 4 (\frac{1}{4} (x - 12))$

Step 3

Simplify the left side.

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Step 3.1

Simplify $4 (y - 1)$ .

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Step 3.1.1

Apply the distributive property.

$4 y + 4 \cdot - 1 = 4 (\frac{1}{4} (x - 12))$

Step 3.1.2

Multiply $4$ by $- 1$ .

$4 y - 4 = 4 (\frac{1}{4} (x - 12))$

Step 4

Simplify the right side.

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Step 4.1

Simplify $4 (\frac{1}{4} (x - 12))$ .

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Step 4.1.1

Apply the distributive property.

$4 y - 4 = 4 (\frac{1}{4} x + \frac{1}{4} \cdot - 12)$

Step 4.1.2

Combine $\frac{1}{4}$ and $x$ .

$4 y - 4 = 4 (\frac{x}{4} + \frac{1}{4} \cdot - 12)$

Step 4.1.3

Cancel the common factor of $4$ .

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Step 4.1.3.1

Factor $4$ out of $- 12$ .

$4 y - 4 = 4 (\frac{x}{4} + \frac{1}{4} \cdot (4 (- 3)))$

Step 4.1.3.2

Cancel the common factor.

$4 y - 4 = 4 (\frac{x}{4} + \frac{1}{4} \cdot (4 \cdot - 3))$

Step 4.1.3.3

Rewrite the expression.

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

Step 4.1.4

Apply the distributive property.

$4 y - 4 = 4 \frac{x}{4} + 4 \cdot - 3$

Step 4.1.5

Cancel the common factor of $4$ .

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Step 4.1.5.1

Cancel the common factor.

$4 y - 4 = 4 \frac{x}{4} + 4 \cdot - 3$

Step 4.1.5.2

Rewrite the expression.

$4 y - 4 = x + 4 \cdot - 3$

Step 4.1.6

Multiply $4$ by $- 3$ .

$4 y - 4 = x - 12$

Step 5

Rewrite the equation.

$x - 12 = 4 y - 4$

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.

$x - 12 - 4 y = - 4$

Step 6.2

Move $- 12$ .

$x - 4 y - 12 = - 4$

Step 7

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

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Step 7.1

Add $12$ to both sides of the equation.

$x - 4 y = - 4 + 12$

Step 7.2

Add $- 4$ and $12$ .

$x - 4 y = 8$

Step 8