Solve the Inequality for x 19>=-2x+5>11

$19 \geq - 2 x + 5 > 11$

Step 1

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

Subtract $5$ from each section of the inequality because it does not contain the variable we are trying to solve for.

$19 - 5 \geq - 2 x > 11 - 5$

Subtract $5$ from $19$ .

$14 \geq - 2 x > 11 - 5$

Subtract $5$ from $11$ .

$14 \geq - 2 x > 6$

Step 2

Divide each term in the inequality by $- 2$ .

$\frac{14}{- 2} \leq \frac{- 2 x}{- 2} < \frac{6}{- 2}$

Step 3

Divide $14$ by $- 2$ .

$- 7 \leq \frac{- 2 x}{- 2} < \frac{6}{- 2}$

Step 4

Cancel the common factor of $- 2$ .

Cancel the common factor.

$- 7 \leq \frac{- 2 x}{- 2} < \frac{6}{- 2}$

Divide $x$ by $1$ .

$- 7 \leq x < \frac{6}{- 2}$

Step 5

Divide $6$ by $- 2$ .

$- 7 \leq x < - 3$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$- 7 \leq x < - 3$

Interval Notation:

$[- 7, - 3)$

Step 7