Basic Math Examples

$2 x + 4 y + z = 22$

Step 1

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

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Step 1.1

Subtract $2 x$ from both sides of the equation.

$4 y + z = 22 - 2 x$

Step 1.2

Subtract $z$ from both sides of the equation.

$4 y = 22 - 2 x - z$

Step 2

Divide each term in $4 y = 22 - 2 x - z$ by $4$ and simplify.

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Step 2.1

Divide each term in $4 y = 22 - 2 x - z$ by $4$ .

$\frac{4 y}{4} = \frac{22}{4} + \frac{- 2 x}{4} + \frac{- z}{4}$

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.

$\frac{4 y}{4} = \frac{22}{4} + \frac{- 2 x}{4} + \frac{- z}{4}$

Step 2.2.1.2

Divide $y$ by $1$ .

$y = \frac{22}{4} + \frac{- 2 x}{4} + \frac{- z}{4}$

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 $22$ and $4$ .

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Step 2.3.1.1.1

Factor $2$ out of $22$ .

$y = \frac{2 (11)}{4} + \frac{- 2 x}{4} + \frac{- z}{4}$

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 $4$ .

$y = \frac{2 \cdot 11}{2 \cdot 2} + \frac{- 2 x}{4} + \frac{- z}{4}$

Step 2.3.1.1.2.2

Cancel the common factor.

$y = \frac{2 \cdot 11}{2 \cdot 2} + \frac{- 2 x}{4} + \frac{- z}{4}$

Step 2.3.1.1.2.3

Rewrite the expression.

$y = \frac{11}{2} + \frac{- 2 x}{4} + \frac{- z}{4}$

Step 2.3.1.2

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

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Step 2.3.1.2.1

Factor $2$ out of $- 2 x$ .

$y = \frac{11}{2} + \frac{2 (- x)}{4} + \frac{- z}{4}$

Step 2.3.1.2.2

Cancel the common factors.

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Step 2.3.1.2.2.1

Factor $2$ out of $4$ .

$y = \frac{11}{2} + \frac{2 (- x)}{2 (2)} + \frac{- z}{4}$

Step 2.3.1.2.2.2

Cancel the common factor.

$y = \frac{11}{2} + \frac{2 (- x)}{2 \cdot 2} + \frac{- z}{4}$

Step 2.3.1.2.2.3

Rewrite the expression.

$y = \frac{11}{2} + \frac{- x}{2} + \frac{- z}{4}$

Step 2.3.1.3

Move the negative in front of the fraction.

$y = \frac{11}{2} - \frac{x}{2} + \frac{- z}{4}$

Step 2.3.1.4

Move the negative in front of the fraction.

$y = \frac{11}{2} - \frac{x}{2} - \frac{z}{4}$