Algebra Examples

$- 1 < \frac{- x - 4}{5} \leq 1$

Step 1

Factor $- 1$ out of $- x$ .

$- 1 < \frac{- (x) - 4}{5} \leq 1$

Step 2

Rewrite $- 4$ as $- 1 (4)$ .

$- 1 < \frac{- (x) - 1 \cdot 4}{5} \leq 1$

Step 3

Factor $- 1$ out of $- (x) - 1 (4)$ .

$- 1 < \frac{- (x + 4)}{5} \leq 1$

Step 4

Simplify the expression.

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Step 4.1

Rewrite $- (x + 4)$ as $- 1 (x + 4)$ .

$- 1 < \frac{- 1 (x + 4)}{5} \leq 1$

Step 4.2

Move the negative in front of the fraction.

$- 1 < - \frac{x + 4}{5} \leq 1$

Step 5

Multiply each term in the inequality by $5$ .

$- 1 \cdot 5 < - \frac{x + 4}{5} \cdot 5 \leq 1 \cdot 5$

Step 6

Multiply $- 1$ by $5$ .

$- 5 < - \frac{x + 4}{5} \cdot 5 \leq 1 \cdot 5$

Step 7

Cancel the common factor of $5$ .

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Step 7.1

Move the leading negative in $- \frac{x + 4}{5}$ into the numerator.

$- 5 < \frac{- (x + 4)}{5} \cdot 5 \leq 1 \cdot 5$

Step 7.2

Cancel the common factor.

$- 5 < \frac{- (x + 4)}{5} \cdot 5 \leq 1 \cdot 5$

Step 7.3

Rewrite the expression.

$- 5 < - (x + 4) \leq 1 \cdot 5$

Step 8

Apply the distributive property.

$- 5 < - x - 1 \cdot 4 \leq 1 \cdot 5$

Step 9

Multiply $- 1$ by $4$ .

$- 5 < - x - 4 \leq 1 \cdot 5$

Step 10

Multiply $5$ by $1$ .

$- 5 < - x - 4 \leq 5$

Step 11

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

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Step 11.1

Add $4$ to each section of the inequality because it does not contain the variable we are trying to solve for.

$- 5 + 4 < - x \leq 5 + 4$

Step 11.2

Add $- 5$ and $4$ .

$- 1 < - x \leq 5 + 4$

Step 11.3

Add $5$ and $4$ .

$- 1 < - x \leq 9$

Step 12

Multiply each term in the inequality by $- 1$ .

$\frac{- 1}{- 1} > \frac{- x}{- 1} \geq \frac{9}{- 1}$

Step 13

Divide $- 1$ by $- 1$ .

$1 > \frac{- x}{- 1} \geq \frac{9}{- 1}$

Step 14

Dividing two negative values results in a positive value.

$1 > \frac{x}{1} \geq \frac{9}{- 1}$

Step 15

Divide $x$ by $1$ .

$1 > x \geq \frac{9}{- 1}$

Step 16

Divide $9$ by $- 1$ .

$1 > x \geq - 9$

Step 17

Rewrite the interval so that the left value is less than the right value. This is the correct way to write an interval solution.

$- 9 \leq x < 1$

Step 18

The result can be shown in multiple forms.

Inequality Form:

$- 9 \leq x < 1$

Interval Notation:

$[- 9, 1)$

Step 19