Solve the System of Inequalities 3x+2<-4 or 4x+4>24

$3 x + 2 < - 4$ or $4 x + 4 > 24$

Simplify the first inequality.

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

Subtract $2$ from both sides of the inequality.

$3 x < - 4 - 2$ or $4 x + 4 > 24$

Subtract $2$ from $- 4$ .

$3 x < - 6$ or $4 x + 4 > 24$

Divide each term in $3 x < - 6$ by $3$ and simplify.

Divide each term in $3 x < - 6$ by $3$ .

$\frac{3 x}{3} < \frac{- 6}{3}$ or $4 x + 4 > 24$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} < \frac{- 6}{3}$ or $4 x + 4 > 24$

Divide $x$ by $1$ .

$x < \frac{- 6}{3}$ or $4 x + 4 > 24$

Simplify the right side.

Divide $- 6$ by $3$ .

$x < - 2$ or $4 x + 4 > 24$

Simplify the second inequality.

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

Subtract $4$ from both sides of the inequality.

$x < - 2$ or $4 x > 24 - 4$

Subtract $4$ from $24$ .

$x < - 2$ or $4 x > 20$

Divide each term in $4 x > 20$ by $4$ and simplify.

Divide each term in $4 x > 20$ by $4$ .

$x < - 2$ or $\frac{4 x}{4} > \frac{20}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$x < - 2$ or $\frac{4 x}{4} > \frac{20}{4}$

Divide $x$ by $1$ .

$x < - 2$ or $x > \frac{20}{4}$

Simplify the right side.

Divide $20$ by $4$ .

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

The result can be shown in multiple forms.

Inequality Form:

$x < - 2 or x > 5$

Interval Notation:

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