Solve for x 9<=6x+6<18

$9 \leq 6 x + 6 < 18$

Step 1

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

Subtract $6$ from each section of the inequality because it does not contain the variable we are trying to solve for.

$9 - 6 \leq 6 x < 18 - 6$

Subtract $6$ from $9$ .

$3 \leq 6 x < 18 - 6$

Subtract $6$ from $18$ .

$3 \leq 6 x < 12$

Step 2

Divide each term in the inequality by $6$ .

$\frac{3}{6} \leq \frac{6 x}{6} < \frac{12}{6}$

Step 3

Cancel the common factor of $3$ and $6$ .

Factor $3$ out of $3$ .

$\frac{3 (1)}{6} \leq \frac{6 x}{6} < \frac{12}{6}$

Cancel the common factors.

Factor $3$ out of $6$ .

$\frac{3 \cdot 1}{3 \cdot 2} \leq \frac{6 x}{6} < \frac{12}{6}$

Cancel the common factor.

$\frac{3 \cdot 1}{3 \cdot 2} \leq \frac{6 x}{6} < \frac{12}{6}$

Rewrite the expression.

$\frac{1}{2} \leq \frac{6 x}{6} < \frac{12}{6}$

Step 4

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{1}{2} \leq \frac{6 x}{6} < \frac{12}{6}$

Divide $x$ by $1$ .

$\frac{1}{2} \leq x < \frac{12}{6}$

Step 5

Divide $12$ by $6$ .

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

Step 6

The result can be shown in multiple forms.

Inequality Form:

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

Interval Notation:

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

Step 7