Solve the System of Inequalities -2x-3<-5 and -11<=-2x-3

$- 2 x - 3 < - 5$ and $- 11 \leq - 2 x - 3$

Step 1

Simplify the first inequality.

Move all terms not containing $x$ to the right side of the inequality.

Add $3$ to both sides of the inequality.

$- 2 x < - 5 + 3$ and $- 11 \leq - 2 x - 3$

Add $- 5$ and $3$ .

$- 2 x < - 2$ and $- 11 \leq - 2 x - 3$

Divide each term in $- 2 x < - 2$ by $- 2$ and simplify.

Divide each term in $- 2 x < - 2$ by $- 2$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 2 x}{- 2} > \frac{- 2}{- 2}$ and $- 11 \leq - 2 x - 3$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 x}{- 2} > \frac{- 2}{- 2}$ and $- 11 \leq - 2 x - 3$

Divide $x$ by $1$ .

$x > \frac{- 2}{- 2}$ and $- 11 \leq - 2 x - 3$

Simplify the right side.

Divide $- 2$ by $- 2$ .

$x > 1$ and $- 11 \leq - 2 x - 3$

Step 2

Simplify the second inequality.

Rewrite so $x$ is on the left side of the inequality.

$x > 1$ and $- 2 x - 3 \geq - 11$

Move all terms not containing $x$ to the right side of the inequality.

Add $3$ to both sides of the inequality.

$x > 1$ and $- 2 x \geq - 11 + 3$

Add $- 11$ and $3$ .

$x > 1$ and $- 2 x \geq - 8$

Divide each term in $- 2 x \geq - 8$ by $- 2$ and simplify.

Divide each term in $- 2 x \geq - 8$ by $- 2$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$x > 1$ and $\frac{- 2 x}{- 2} \leq \frac{- 8}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$x > 1$ and $\frac{- 2 x}{- 2} \leq \frac{- 8}{- 2}$

Divide $x$ by $1$ .

$x > 1$ and $x \leq \frac{- 8}{- 2}$

Simplify the right side.

Divide $- 8$ by $- 2$ .

$x > 1$ and $x \leq 4$

Step 3

The intersection consists of the elements that are contained in both intervals.

$1 < x \leq 4$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$1 < x \leq 4$

Interval Notation:

$(1, 4]$

Step 5

Solve the System of Inequalities -2x-3<-5 and -11<=-2x-3

Related Questions

Support LCMGCF.com by disabling your adblocker.