Solve the System of Inequalities 2x-9<-27 or -21<2x-9

$2 x - 9 < - 27$ or $- 21 < 2 x - 9$

Step 1

Simplify the first inequality.

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

Add $9$ to both sides of the inequality.

$2 x < - 27 + 9$ or $- 21 < 2 x - 9$

Add $- 27$ and $9$ .

$2 x < - 18$ or $- 21 < 2 x - 9$

Divide each term in $2 x < - 18$ by $2$ and simplify.

Divide each term in $2 x < - 18$ by $2$ .

$\frac{2 x}{2} < \frac{- 18}{2}$ or $- 21 < 2 x - 9$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} < \frac{- 18}{2}$ or $- 21 < 2 x - 9$

Divide $x$ by $1$ .

$x < \frac{- 18}{2}$ or $- 21 < 2 x - 9$

Simplify the right side.

Divide $- 18$ by $2$ .

$x < - 9$ or $- 21 < 2 x - 9$

Step 2

Simplify the second inequality.

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

$x < - 9$ or $2 x - 9 > - 21$

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

Add $9$ to both sides of the inequality.

$x < - 9$ or $2 x > - 21 + 9$

Add $- 21$ and $9$ .

$x < - 9$ or $2 x > - 12$

Divide each term in $2 x > - 12$ by $2$ and simplify.

Divide each term in $2 x > - 12$ by $2$ .

$x < - 9$ or $\frac{2 x}{2} > \frac{- 12}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$x < - 9$ or $\frac{2 x}{2} > \frac{- 12}{2}$

Divide $x$ by $1$ .

$x < - 9$ or $x > \frac{- 12}{2}$

Simplify the right side.

Divide $- 12$ by $2$ .

$x < - 9$ or $x > - 6$

Step 3

The result can be shown in multiple forms.

Inequality Form:

$x < - 9 or x > - 6$

Interval Notation:

$(- \infty, - 9) \cup (- 6, \infty)$

Step 4

Solve the System of Inequalities 2x-9<-27 or -21<2x-9

Related Questions

Support LCMGCF.com by disabling your adblocker.