Solve the System of @WORD -2<=2x-5<4

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

Step 1

Solve $- 2 \leq 2 x - 5$ for $x$ .

Rewrite so $x$ is on the left side of the inequality.

$2 x - 5 \geq - 2$

Move all terms not containing $x$ to the right side of the inequality.

Add $5$ to both sides of the inequality.

$2 x \geq - 2 + 5$

Add $- 2$ and $5$ .

$2 x \geq 3$

Divide each term in $2 x \geq 3$ by $2$ and simplify.

Divide each term in $2 x \geq 3$ by $2$ .

$\frac{2 x}{2} \geq \frac{3}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} \geq \frac{3}{2}$

Divide $x$ by $1$ .

$x \geq \frac{3}{2}$

Step 2

Solve $2 x - 5 < 4$ for $x$ .

Move all terms not containing $x$ to the right side of the inequality.

Add $5$ to both sides of the inequality.

$2 x < 4 + 5$

Add $4$ and $5$ .

$2 x < 9$

Divide each term in $2 x < 9$ by $2$ and simplify.

Divide each term in $2 x < 9$ by $2$ .

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

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Step 3

Find the intersection of $x \geq \frac{3}{2}$ and $x < \frac{9}{2}$ .

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

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