Basic Math Examples

$3 x + 2 y - z = 1$

Step 1

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

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Step 1.1

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

$2 y - z = 1 - 3 x$

Step 1.2

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

$- z = 1 - 3 x - 2 y$

Step 2

Divide each term in $- z = 1 - 3 x - 2 y$ by $- 1$ and simplify.

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Step 2.1

Divide each term in $- z = 1 - 3 x - 2 y$ by $- 1$ .

$\frac{- z}{- 1} = \frac{1}{- 1} + \frac{- 3 x}{- 1} + \frac{- 2 y}{- 1}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Dividing two negative values results in a positive value.

$\frac{z}{1} = \frac{1}{- 1} + \frac{- 3 x}{- 1} + \frac{- 2 y}{- 1}$

Step 2.2.2

Divide $z$ by $1$ .

$z = \frac{1}{- 1} + \frac{- 3 x}{- 1} + \frac{- 2 y}{- 1}$

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

Divide $1$ by $- 1$ .

$z = - 1 + \frac{- 3 x}{- 1} + \frac{- 2 y}{- 1}$

Step 2.3.1.2

Move the negative one from the denominator of $\frac{- 3 x}{- 1}$ .

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

Step 2.3.1.3

Rewrite $- 1 \cdot (- 3 x)$ as $- (- 3 x)$ .

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

Step 2.3.1.4

Multiply $- 3$ by $- 1$ .

$z = - 1 + 3 x + \frac{- 2 y}{- 1}$

Step 2.3.1.5

Move the negative one from the denominator of $\frac{- 2 y}{- 1}$ .

$z = - 1 + 3 x - 1 \cdot (- 2 y)$

Step 2.3.1.6

Rewrite $- 1 \cdot (- 2 y)$ as $- (- 2 y)$ .

$z = - 1 + 3 x - (- 2 y)$

Step 2.3.1.7

Multiply $- 2$ by $- 1$ .

$z = - 1 + 3 x + 2 y$