Solve for x -4<=2x-3<4

$- 4 \leq 2 x - 3 < 4$

Step 1

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

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

$- 4 + 3 \leq 2 x < 4 + 3$

Add $- 4$ and $3$ .

$- 1 \leq 2 x < 4 + 3$

Add $4$ and $3$ .

$- 1 \leq 2 x < 7$

Step 2

Divide each term in the inequality by $2$ .

$\frac{- 1}{2} \leq \frac{2 x}{2} < \frac{7}{2}$

Step 3

Move the negative in front of the fraction.

$- \frac{1}{2} \leq \frac{2 x}{2} < \frac{7}{2}$

Step 4

Cancel the common factor of $2$ .

Cancel the common factor.

$- \frac{1}{2} \leq \frac{2 x}{2} < \frac{7}{2}$

Divide $x$ by $1$ .

$- \frac{1}{2} \leq x < \frac{7}{2}$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$- \frac{1}{2} \leq x < \frac{7}{2}$

Interval Notation:

$[- \frac{1}{2}, \frac{7}{2})$

Step 6