Solve the System of Inequalities 2x-2<-12 or 2x+3>7

$2 x - 2 < - 12$ or $2 x + 3 > 7$

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.

$2 x < - 12 + 2$ or $2 x + 3 > 7$

Add $- 12$ and $2$ .

$2 x < - 10$ or $2 x + 3 > 7$

Divide each term in $2 x < - 10$ by $2$ and simplify.

Divide each term in $2 x < - 10$ by $2$ .

$\frac{2 x}{2} < \frac{- 10}{2}$ or $2 x + 3 > 7$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} < \frac{- 10}{2}$ or $2 x + 3 > 7$

Divide $x$ by $1$ .

$x < \frac{- 10}{2}$ or $2 x + 3 > 7$

Simplify the right side.

Divide $- 10$ by $2$ .

$x < - 5$ or $2 x + 3 > 7$

Step 2

Simplify the second inequality.

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

Subtract $3$ from both sides of the inequality.

$x < - 5$ or $2 x > 7 - 3$

Subtract $3$ from $7$ .

$x < - 5$ or $2 x > 4$

Divide each term in $2 x > 4$ by $2$ and simplify.

Divide each term in $2 x > 4$ by $2$ .

$x < - 5$ or $\frac{2 x}{2} > \frac{4}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$x < - 5$ or $\frac{2 x}{2} > \frac{4}{2}$

Divide $x$ by $1$ .

$x < - 5$ or $x > \frac{4}{2}$

Simplify the right side.

Divide $4$ by $2$ .

$x < - 5$ or $x > 2$

Step 3

The result can be shown in multiple forms.

Inequality Form:

$x < - 5 or x > 2$

Interval Notation:

$(- \infty, - 5) \cup (2, \infty)$

Step 4

Solve the System of Inequalities 2x-2<-12 or 2x+3>7

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