Solve for x -2<3-2x<7

$- 2 < 3 - 2 x < 7$

Step 1

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

Subtract $3$ from each section of the inequality because it does not contain the variable we are trying to solve for.

$- 2 - 3 < - 2 x < 7 - 3$

Subtract $3$ from $- 2$ .

$- 5 < - 2 x < 7 - 3$

Subtract $3$ from $7$ .

$- 5 < - 2 x < 4$

Step 2

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

$\frac{- 5}{- 2} > \frac{- 2 x}{- 2} > \frac{4}{- 2}$

Step 3

Dividing two negative values results in a positive value.

$\frac{5}{2} > \frac{- 2 x}{- 2} > \frac{4}{- 2}$

Step 4

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{5}{2} > \frac{- 2 x}{- 2} > \frac{4}{- 2}$

Divide $x$ by $1$ .

$\frac{5}{2} > x > \frac{4}{- 2}$

Step 5

Divide $4$ by $- 2$ .

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

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.

$- 2 < x < \frac{5}{2}$

Step 7

The result can be shown in multiple forms.

Inequality Form:

$- 2 < x < \frac{5}{2}$

Interval Notation:

$(- 2, \frac{5}{2})$

Step 8