Basic Math Examples

$q = 100 - w + 0.5 z$

Step 1

Rewrite the equation as $100 - w + 0.5 z = q$ .

$100 - w + 0.5 z = q$

Step 2

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

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Step 2.1

Subtract $100$ from both sides of the equation.

$- w + 0.5 z = q - 100$

Step 2.2

Subtract $0.5 z$ from both sides of the equation.

$- w = q - 100 - 0.5 z$

Step 3

Divide each term in $- w = q - 100 - 0.5 z$ by $- 1$ and simplify.

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Step 3.1

Divide each term in $- w = q - 100 - 0.5 z$ by $- 1$ .

$\frac{- w}{- 1} = \frac{q}{- 1} + \frac{- 100}{- 1} + \frac{- 0.5 z}{- 1}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Dividing two negative values results in a positive value.

$\frac{w}{1} = \frac{q}{- 1} + \frac{- 100}{- 1} + \frac{- 0.5 z}{- 1}$

Step 3.2.2

Divide $w$ by $1$ .

$w = \frac{q}{- 1} + \frac{- 100}{- 1} + \frac{- 0.5 z}{- 1}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Simplify each term.

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Step 3.3.1.1

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

$w = - 1 \cdot q + \frac{- 100}{- 1} + \frac{- 0.5 z}{- 1}$

Step 3.3.1.2

Rewrite $- 1 \cdot q$ as $- q$ .

$w = - q + \frac{- 100}{- 1} + \frac{- 0.5 z}{- 1}$

Step 3.3.1.3

Divide $- 100$ by $- 1$ .

$w = - q + 100 + \frac{- 0.5 z}{- 1}$

Step 3.3.1.4

Move the negative one from the denominator of $\frac{- 0.5 z}{- 1}$ .

$w = - q + 100 - 1 \cdot (- 0.5 z)$

Step 3.3.1.5

Rewrite $- 1 \cdot (- 0.5 z)$ as $- (- 0.5 z)$ .

$w = - q + 100 - (- 0.5 z)$

Step 3.3.1.6

Multiply $- 0.5$ by $- 1$ .

$w = - q + 100 + 0.5 z$