Solve the System of Inequalities 2x-2<-4 or 2x-2>=20

$2 x - 2 < - 4$ or $2 x - 2 \geq 20$

Step 1

Simplify the first inequality.

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

Add $2$ to both sides of the inequality.

$2 x < - 4 + 2$ or $2 x - 2 \geq 20$

Add $- 4$ and $2$ .

$2 x < - 2$ or $2 x - 2 \geq 20$

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

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

$\frac{2 x}{2} < \frac{- 2}{2}$ or $2 x - 2 \geq 20$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} < \frac{- 2}{2}$ or $2 x - 2 \geq 20$

Divide $x$ by $1$ .

$x < \frac{- 2}{2}$ or $2 x - 2 \geq 20$

Simplify the right side.

Divide $- 2$ by $2$ .

$x < - 1$ or $2 x - 2 \geq 20$

Step 2

Simplify the second inequality.

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

Add $2$ to both sides of the inequality.

$x < - 1$ or $2 x \geq 20 + 2$

Add $20$ and $2$ .

$x < - 1$ or $2 x \geq 22$

Divide each term in $2 x \geq 22$ by $2$ and simplify.

Divide each term in $2 x \geq 22$ by $2$ .

$x < - 1$ or $\frac{2 x}{2} \geq \frac{22}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$x < - 1$ or $\frac{2 x}{2} \geq \frac{22}{2}$

Divide $x$ by $1$ .

$x < - 1$ or $x \geq \frac{22}{2}$

Simplify the right side.

Divide $22$ by $2$ .

$x < - 1$ or $x \geq 11$

Step 3

The result can be shown in multiple forms.

Inequality Form:

$x < - 1 or x \geq 11$

Interval Notation:

$(- \infty, - 1) \cup [11, \infty)$

Step 4

Solve the System of Inequalities 2x-2<-4 or 2x-2>=20

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