Solve for x -6<=3x-9<0

$- 6 \leq 3 x - 9 < 0$

Step 1

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

Add $9$ to each section of the inequality because it does not contain the variable we are trying to solve for.

$- 6 + 9 \leq 3 x < 0 + 9$

Add $- 6$ and $9$ .

$3 \leq 3 x < 0 + 9$

Add $0$ and $9$ .

$3 \leq 3 x < 9$

Step 2

Divide each term in the inequality by $3$ .

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

Step 3

Divide $3$ by $3$ .

$1 \leq \frac{3 x}{3} < \frac{9}{3}$

Step 4

Cancel the common factor of $3$ .

Cancel the common factor.

$1 \leq \frac{3 x}{3} < \frac{9}{3}$

Divide $x$ by $1$ .

$1 \leq x < \frac{9}{3}$

Step 5

Divide $9$ by $3$ .

$1 \leq x < 3$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$1 \leq x < 3$

Interval Notation:

$[1, 3)$

Step 7