Solve for x -2<=2x-5<4

$- 2 \leq 2 x - 5 < 4$

Step 1

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

Add $5$ to each section of the inequality because it does not contain the variable we are trying to solve for.

$- 2 + 5 \leq 2 x < 4 + 5$

Add $- 2$ and $5$ .

$3 \leq 2 x < 4 + 5$

Add $4$ and $5$ .

$3 \leq 2 x < 9$

Step 2

Divide each term in the inequality by $2$ .

$\frac{3}{2} \leq \frac{2 x}{2} < \frac{9}{2}$

Step 3

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{3}{2} \leq \frac{2 x}{2} < \frac{9}{2}$

Divide $x$ by $1$ .

$\frac{3}{2} \leq x < \frac{9}{2}$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$\frac{3}{2} \leq x < \frac{9}{2}$

Interval Notation:

$[\frac{3}{2}, \frac{9}{2})$

Step 5