Solve for x 3<=2x-3<15

$3 \leq 2 x - 3 < 15$

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.

$3 + 3 \leq 2 x < 15 + 3$

Add $3$ and $3$ .

$6 \leq 2 x < 15 + 3$

Add $15$ and $3$ .

$6 \leq 2 x < 18$

Step 2

Divide each term in the inequality by $2$ .

$\frac{6}{2} \leq \frac{2 x}{2} < \frac{18}{2}$

Step 3

Divide $6$ by $2$ .

$3 \leq \frac{2 x}{2} < \frac{18}{2}$

Step 4

Cancel the common factor of $2$ .

Cancel the common factor.

$3 \leq \frac{2 x}{2} < \frac{18}{2}$

Divide $x$ by $1$ .

$3 \leq x < \frac{18}{2}$

Step 5

Divide $18$ by $2$ .

$3 \leq x < 9$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$3 \leq x < 9$

Interval Notation:

$[3, 9)$

Step 7