Solve for x 2<=2x+4<8

$2 \leq 2 x + 4 < 8$

Step 1

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

Subtract $4$ from each section of the inequality because it does not contain the variable we are trying to solve for.

$2 - 4 \leq 2 x < 8 - 4$

Subtract $4$ from $2$ .

$- 2 \leq 2 x < 8 - 4$

Subtract $4$ from $8$ .

$- 2 \leq 2 x < 4$

Step 2

Divide each term in the inequality by $2$ .

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

Step 3

Divide $- 2$ by $2$ .

$- 1 \leq \frac{2 x}{2} < \frac{4}{2}$

Step 4

Cancel the common factor of $2$ .

Cancel the common factor.

$- 1 \leq \frac{2 x}{2} < \frac{4}{2}$

Divide $x$ by $1$ .

$- 1 \leq x < \frac{4}{2}$

Step 5

Divide $4$ by $2$ .

$- 1 \leq x < 2$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$- 1 \leq x < 2$

Interval Notation:

$[- 1, 2)$

Step 7