Solve for x 6<=2x+2<12

$6 \leq 2 x + 2 < 12$

Step 1

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

Subtract $2$ from each section of the inequality because it does not contain the variable we are trying to solve for.

$6 - 2 \leq 2 x < 12 - 2$

Subtract $2$ from $6$ .

$4 \leq 2 x < 12 - 2$

Subtract $2$ from $12$ .

$4 \leq 2 x < 10$

Step 2

Divide each term in the inequality by $2$ .

$\frac{4}{2} \leq \frac{2 x}{2} < \frac{10}{2}$

Step 3

Divide $4$ by $2$ .

$2 \leq \frac{2 x}{2} < \frac{10}{2}$

Step 4

Cancel the common factor of $2$ .

Cancel the common factor.

$2 \leq \frac{2 x}{2} < \frac{10}{2}$

Divide $x$ by $1$ .

$2 \leq x < \frac{10}{2}$

Step 5

Divide $10$ by $2$ .

$2 \leq x < 5$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$2 \leq x < 5$

Interval Notation:

$[2, 5)$

Step 7