Precalculus Examples

$3 x + 2 y - 2 z = - 13$

Step 1

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

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Step 1.1

Subtract $3 x$ from both sides of the equation.

$2 y - 2 z = - 13 - 3 x$

Step 1.2

Add $2 z$ to both sides of the equation.

$2 y = - 13 - 3 x + 2 z$

Step 2

Divide each term in $2 y = - 13 - 3 x + 2 z$ by $2$ and simplify.

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Step 2.1

Divide each term in $2 y = - 13 - 3 x + 2 z$ by $2$ .

$\frac{2 y}{2} = \frac{- 13}{2} + \frac{- 3 x}{2} + \frac{2 z}{2}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $2$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{2 y}{2} = \frac{- 13}{2} + \frac{- 3 x}{2} + \frac{2 z}{2}$

Step 2.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 13}{2} + \frac{- 3 x}{2} + \frac{2 z}{2}$

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

Move the negative in front of the fraction.

$y = - \frac{13}{2} + \frac{- 3 x}{2} + \frac{2 z}{2}$

Step 2.3.1.2

Move the negative in front of the fraction.

$y = - \frac{13}{2} - \frac{3 x}{2} + \frac{2 z}{2}$

Step 2.3.1.3

Cancel the common factor of $2$ .

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Step 2.3.1.3.1

Cancel the common factor.

$y = - \frac{13}{2} - \frac{3 x}{2} + \frac{2 z}{2}$

Step 2.3.1.3.2

Divide $z$ by $1$ .

$y = - \frac{13}{2} - \frac{3 x}{2} + z$