Algebra Examples

$1 < - x - 1 < 4$

Step 1

Solve $- 2 > x > - 5$ .

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Step 1.1

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

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Step 1.1.1

Add $1$ to each section of the inequality because it does not contain the variable we are trying to solve for.

$1 + 1 < - x < 4 + 1$

Step 1.1.2

Add $1$ and $1$ .

$2 < - x < 4 + 1$

Step 1.1.3

Add $4$ and $1$ .

$2 < - x < 5$

Step 1.2

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

$\frac{2}{- 1} > \frac{- x}{- 1} > \frac{5}{- 1}$

Step 1.3

Divide $2$ by $- 1$ .

$- 2 > \frac{- x}{- 1} > \frac{5}{- 1}$

Step 1.4

Dividing two negative values results in a positive value.

$- 2 > \frac{x}{1} > \frac{5}{- 1}$

Step 1.5

Divide $x$ by $1$ .

$- 2 > x > \frac{5}{- 1}$

Step 1.6

Divide $5$ by $- 1$ .

$- 2 > x > - 5$

Step 1.7

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

$- 5 < x < - 2$

Step 2

Use the inequality $- 5 < x < - 2$ to build the set notation.

${x | - 5 < x < - 2}$

Step 3