Linear Algebra Examples

$y - 2 = 4 (x - 1)$

Step 1

Rewrite the equation as $4 (x - 1) = y - 2$ .

$4 (x - 1) = y - 2$

Step 2

Divide each term in $4 (x - 1) = y - 2$ by $4$ and simplify.

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Step 2.1

Divide each term in $4 (x - 1) = y - 2$ by $4$ .

$\frac{4 (x - 1)}{4} = \frac{y}{4} + \frac{- 2}{4}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $4$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{4 (x - 1)}{4} = \frac{y}{4} + \frac{- 2}{4}$

Step 2.2.1.2

Divide $x - 1$ by $1$ .

$x - 1 = \frac{y}{4} + \frac{- 2}{4}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Simplify each term.

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Step 2.3.1.1

Cancel the common factor of $- 2$ and $4$ .

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Step 2.3.1.1.1

Factor $2$ out of $- 2$ .

$x - 1 = \frac{y}{4} + \frac{2 (- 1)}{4}$

Step 2.3.1.1.2

Cancel the common factors.

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Step 2.3.1.1.2.1

Factor $2$ out of $4$ .

$x - 1 = \frac{y}{4} + \frac{2 \cdot - 1}{2 \cdot 2}$

Step 2.3.1.1.2.2

Cancel the common factor.

$x - 1 = \frac{y}{4} + \frac{2 \cdot - 1}{2 \cdot 2}$

Step 2.3.1.1.2.3

Rewrite the expression.

$x - 1 = \frac{y}{4} + \frac{- 1}{2}$

Step 2.3.1.2

Move the negative in front of the fraction.

$x - 1 = \frac{y}{4} - \frac{1}{2}$

Step 3

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

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Step 3.1

Add $1$ to both sides of the equation.

$x = \frac{y}{4} - \frac{1}{2} + 1$

Step 3.2

Write $1$ as a fraction with a common denominator.

$x = \frac{y}{4} - \frac{1}{2} + \frac{2}{2}$

Step 3.3

Combine the numerators over the common denominator.

$x = \frac{y}{4} + \frac{- 1 + 2}{2}$

Step 3.4

Add $- 1$ and $2$ .

$x = \frac{y}{4} + \frac{1}{2}$