Solve for x 7>=2x+3>=-1

$7 \geq 2 x + 3 \geq - 1$

Step 1

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

Subtract $3$ from each section of the inequality because it does not contain the variable we are trying to solve for.

$7 - 3 \geq 2 x \geq - 1 - 3$

Subtract $3$ from $7$ .

$4 \geq 2 x \geq - 1 - 3$

Subtract $3$ from $- 1$ .

$4 \geq 2 x \geq - 4$

Step 2

Divide each term in the inequality by $2$ .

$\frac{4}{2} \geq \frac{2 x}{2} \geq \frac{- 4}{2}$

Step 3

Divide $4$ by $2$ .

$2 \geq \frac{2 x}{2} \geq \frac{- 4}{2}$

Step 4

Cancel the common factor of $2$ .

Cancel the common factor.

$2 \geq \frac{2 x}{2} \geq \frac{- 4}{2}$

Divide $x$ by $1$ .

$2 \geq x \geq \frac{- 4}{2}$

Step 5

Divide $- 4$ by $2$ .

$2 \geq x \geq - 2$

Step 6

Rewrite the interval so that the left value is less than the right value. This is the correct way to write an interval solution.

$- 2 \leq x \leq 2$

Step 7

The result can be shown in multiple forms.

Inequality Form:

$- 2 \leq x \leq 2$

Interval Notation:

$[- 2, 2]$

Step 8