Finite Math Examples

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

Step 1

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

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Step 1.1

Add $\frac{3}{2}$ to both sides of the inequality.

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

Step 1.2

Combine the numerators over the common denominator.

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

Step 1.3

Add $1$ and $3$ .

$- 2 z < \frac{4}{2}$

Step 1.4

Divide $4$ by $2$ .

$- 2 z < 2$

Step 2

Divide each term in $- 2 z < 2$ by $- 2$ and simplify.

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Step 2.1

Divide each term in $- 2 z < 2$ by $- 2$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 2 z}{- 2} > \frac{2}{- 2}$

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.

$\frac{- 2 z}{- 2} > \frac{2}{- 2}$

Step 2.2.1.2

Divide $z$ by $1$ .

$z > \frac{2}{- 2}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide $2$ by $- 2$ .

$z > - 1$

Step 3

The result can be shown in multiple forms.

Inequality Form:

$z > - 1$

Interval Notation:

$(- 1, \infty)$