Algebra Examples

$- 20 \leq \frac{5}{9} (F - 32) \leq - 15$

Step 1

Apply the distributive property.

$- 20 \leq \frac{5}{9} F + \frac{5}{9} \cdot - 32 \leq - 15$

Step 2

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

$- 20 \leq \frac{5 F}{9} + \frac{5}{9} \cdot - 32 \leq - 15$

Step 3

Multiply $\frac{5}{9} \cdot - 32$ .

Tap for more steps...

Step 3.1

Combine $\frac{5}{9}$ and $- 32$ .

$- 20 \leq \frac{5 F}{9} + \frac{5 \cdot - 32}{9} \leq - 15$

Step 3.2

Multiply $5$ by $- 32$ .

$- 20 \leq \frac{5 F}{9} + \frac{- 160}{9} \leq - 15$

Step 4

Move the negative in front of the fraction.

$- 20 \leq \frac{5 F}{9} - \frac{160}{9} \leq - 15$

Step 5

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

Tap for more steps...

Step 5.1

Add $\frac{160}{9}$ to each section of the inequality because it does not contain the variable we are trying to solve for.

$- 20 + \frac{160}{9} \leq \frac{5 F}{9} \leq - 15 + \frac{160}{9}$

Step 5.2

To write $- 20$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$- 20 \cdot \frac{9}{9} + \frac{160}{9} \leq \frac{5 F}{9} \leq - 15 + \frac{160}{9}$

Step 5.3

Combine $- 20$ and $\frac{9}{9}$ .

$\frac{- 20 \cdot 9}{9} + \frac{160}{9} \leq \frac{5 F}{9} \leq - 15 + \frac{160}{9}$

Step 5.4

Combine the numerators over the common denominator.

$\frac{- 20 \cdot 9 + 160}{9} \leq \frac{5 F}{9} \leq - 15 + \frac{160}{9}$

Step 5.5

Simplify the numerator.

Tap for more steps...

Step 5.5.1

Multiply $- 20$ by $9$ .

$\frac{- 180 + 160}{9} \leq \frac{5 F}{9} \leq - 15 + \frac{160}{9}$

Step 5.5.2

Add $- 180$ and $160$ .

$\frac{- 20}{9} \leq \frac{5 F}{9} \leq - 15 + \frac{160}{9}$

Step 5.6

Move the negative in front of the fraction.

$- \frac{20}{9} \leq \frac{5 F}{9} \leq - 15 + \frac{160}{9}$

Step 5.7

Multiply each term in the inequality by $9$ .

$- \frac{20}{9} \cdot 9 \leq \frac{5 F}{9} \cdot 9 \leq - 15 \cdot 9 + \frac{160}{9} \cdot 9$

Step 5.8

Cancel the common factor of $9$ .

Tap for more steps...

Step 5.8.1

Move the leading negative in $- \frac{20}{9}$ into the numerator.

$\frac{- 20}{9} \cdot 9 \leq \frac{5 F}{9} \cdot 9 \leq - 15 \cdot 9 + \frac{160}{9} \cdot 9$

Step 5.8.2

Cancel the common factor.

$\frac{- 20}{9} \cdot 9 \leq \frac{5 F}{9} \cdot 9 \leq - 15 \cdot 9 + \frac{160}{9} \cdot 9$

Step 5.8.3

Rewrite the expression.

$- 20 \leq \frac{5 F}{9} \cdot 9 \leq - 15 \cdot 9 + \frac{160}{9} \cdot 9$

Step 5.9

Cancel the common factor of $9$ .

Tap for more steps...

Step 5.9.1

Cancel the common factor.

$- 20 \leq \frac{5 F}{9} \cdot 9 \leq - 15 \cdot 9 + \frac{160}{9} \cdot 9$

Step 5.9.2

Rewrite the expression.

$- 20 \leq 5 F \leq - 15 \cdot 9 + \frac{160}{9} \cdot 9$

Step 5.10

Simplify each term.

Tap for more steps...

Step 5.10.1

Multiply $- 15$ by $9$ .

$- 20 \leq 5 F \leq - 135 + \frac{160}{9} \cdot 9$

Step 5.10.2

Cancel the common factor of $9$ .

Tap for more steps...

Step 5.10.2.1

Cancel the common factor.

$- 20 \leq 5 F \leq - 135 + \frac{160}{9} \cdot 9$

Step 5.10.2.2

Rewrite the expression.

$- 20 \leq 5 F \leq - 135 + 160$

Step 5.11

Add $- 135$ and $160$ .

$- 20 \leq 5 F \leq 25$

Step 6

Divide each term in the inequality by $5$ .

$\frac{- 20}{5} \leq \frac{5 F}{5} \leq \frac{25}{5}$

Step 7

Divide $- 20$ by $5$ .

$- 4 \leq \frac{5 F}{5} \leq \frac{25}{5}$

Step 8

Cancel the common factor of $5$ .

Tap for more steps...

Step 8.1

Cancel the common factor.

$- 4 \leq \frac{5 F}{5} \leq \frac{25}{5}$

Step 8.2

Divide $F$ by $1$ .

$- 4 \leq F \leq \frac{25}{5}$

Step 9

Divide $25$ by $5$ .

$- 4 \leq F \leq 5$

Step 10

The result can be shown in multiple forms.

Inequality Form:

$- 4 \leq F \leq 5$

Interval Notation:

$[- 4, 5]$

Step 11