Finite Math Examples

$- 4 \leq \frac{9}{5} c + 32 \leq 68$

Step 1

Combine $\frac{9}{5}$ and $c$ .

$- 4 \leq \frac{9 c}{5} + 32 \leq 68$

Step 2

Move all terms not containing $c$ from the center section of the inequality.

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Step 2.1

Subtract $32$ from each section of the inequality because it does not contain the variable we are trying to solve for.

$- 4 - 32 \leq \frac{9 c}{5} \leq 68 - 32$

Step 2.2

Subtract $32$ from $- 4$ .

$- 36 \leq \frac{9 c}{5} \leq 68 - 32$

Step 2.3

Multiply each term in the inequality by $5$ .

$- 36 \cdot 5 \leq \frac{9 c}{5} \cdot 5 \leq 68 \cdot 5 - 32 \cdot 5$

Step 2.4

Multiply $- 36$ by $5$ .

$- 180 \leq \frac{9 c}{5} \cdot 5 \leq 68 \cdot 5 - 32 \cdot 5$

Step 2.5

Cancel the common factor of $5$ .

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Step 2.5.1

Cancel the common factor.

$- 180 \leq \frac{9 c}{5} \cdot 5 \leq 68 \cdot 5 - 32 \cdot 5$

Step 2.5.2

Rewrite the expression.

$- 180 \leq 9 c \leq 68 \cdot 5 - 32 \cdot 5$

Step 2.6

Simplify each term.

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Step 2.6.1

Multiply $68$ by $5$ .

$- 180 \leq 9 c \leq 340 - 32 \cdot 5$

Step 2.6.2

Multiply $- 32$ by $5$ .

$- 180 \leq 9 c \leq 340 - 160$

Step 2.7

Subtract $160$ from $340$ .

$- 180 \leq 9 c \leq 180$

Step 3

Divide each term in the inequality by $9$ .

$\frac{- 180}{9} \leq \frac{9 c}{9} \leq \frac{180}{9}$

Step 4

Divide $- 180$ by $9$ .

$- 20 \leq \frac{9 c}{9} \leq \frac{180}{9}$

Step 5

Cancel the common factor of $9$ .

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Step 5.1

Cancel the common factor.

$- 20 \leq \frac{9 c}{9} \leq \frac{180}{9}$

Step 5.2

Divide $c$ by $1$ .

$- 20 \leq c \leq \frac{180}{9}$

Step 6

Divide $180$ by $9$ .

$- 20 \leq c \leq 20$

Step 7

The result can be shown in multiple forms.

Inequality Form:

$- 20 \leq c \leq 20$

Interval Notation:

$[- 20, 20]$

Step 8