Pre-Algebra Examples

$- 4 < - 2 x + 2 < 12$

Step 1

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

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Step 1.1

Subtract $2$ from each section of the inequality because it does not contain the variable we are trying to solve for.

$- 4 - 2 < - 2 x < 12 - 2$

Step 1.2

Subtract $2$ from $- 4$ .

$- 6 < - 2 x < 12 - 2$

Step 1.3

Subtract $2$ from $12$ .

$- 6 < - 2 x < 10$

Step 2

Divide each term in the inequality by $- 2$ .

$\frac{- 6}{- 2} > \frac{- 2 x}{- 2} > \frac{10}{- 2}$

Step 3

Divide $- 6$ by $- 2$ .

$3 > \frac{- 2 x}{- 2} > \frac{10}{- 2}$

Step 4

Cancel the common factor of $- 2$ .

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Step 4.1

Cancel the common factor.

$3 > \frac{- 2 x}{- 2} > \frac{10}{- 2}$

Step 4.2

Divide $x$ by $1$ .

$3 > x > \frac{10}{- 2}$

Step 5

Divide $10$ by $- 2$ .

$3 > x > - 5$

Step 6

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

$- 5 < x < 3$

Step 7