Finite Math Examples

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

Step 1

Rewrite the equation as $z (\frac{1}{2}) + 1 = - \frac{3}{2}$ .

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

Step 2

Combine $z$ and $\frac{1}{2}$ .

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

Step 3

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

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Step 3.1

Subtract $1$ from both sides of the equation.

$\frac{z}{2} = - \frac{3}{2} - 1$

Step 3.2

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{z}{2} = - \frac{3}{2} - 1 \cdot \frac{2}{2}$

Step 3.3

Combine $- 1$ and $\frac{2}{2}$ .

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

Step 3.4

Combine the numerators over the common denominator.

$\frac{z}{2} = \frac{- 3 - 1 \cdot 2}{2}$

Step 3.5

Simplify the numerator.

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Step 3.5.1

Multiply $- 1$ by $2$ .

$\frac{z}{2} = \frac{- 3 - 2}{2}$

Step 3.5.2

Subtract $2$ from $- 3$ .

$\frac{z}{2} = \frac{- 5}{2}$

Step 3.6

Move the negative in front of the fraction.

$\frac{z}{2} = - \frac{5}{2}$

Step 4

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$z = - 5$