Solve for x -4<=2x-1<=5

$- 4 \leq 2 x - 1 \leq 5$

Step 1

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

Add $1$ to each section of the inequality because it does not contain the variable we are trying to solve for.

$- 4 + 1 \leq 2 x \leq 5 + 1$

Add $- 4$ and $1$ .

$- 3 \leq 2 x \leq 5 + 1$

Add $5$ and $1$ .

$- 3 \leq 2 x \leq 6$

Step 2

Divide each term in the inequality by $2$ .

$\frac{- 3}{2} \leq \frac{2 x}{2} \leq \frac{6}{2}$

Step 3

Move the negative in front of the fraction.

$- \frac{3}{2} \leq \frac{2 x}{2} \leq \frac{6}{2}$

Step 4

Cancel the common factor of $2$ .

Cancel the common factor.

$- \frac{3}{2} \leq \frac{2 x}{2} \leq \frac{6}{2}$

Divide $x$ by $1$ .

$- \frac{3}{2} \leq x \leq \frac{6}{2}$

Step 5

Divide $6$ by $2$ .

$- \frac{3}{2} \leq x \leq 3$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$- \frac{3}{2} \leq x \leq 3$

Interval Notation:

$[- \frac{3}{2}, 3]$

Step 7