Solve the System of Inequalities -8<2(x+4) or -3x+4>x-4

$- 8 < 2 (x + 4)$ or $- 3 x + 4 > x - 4$

Step 1

Simplify the first inequality.

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

$2 (x + 4) > - 8$ or $- 3 x + 4 > x - 4$

Divide each term in $2 (x + 4) > - 8$ by $2$ and simplify.

Divide each term in $2 (x + 4) > - 8$ by $2$ .

$\frac{2 (x + 4)}{2} > \frac{- 8}{2}$ or $- 3 x + 4 > x - 4$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 (x + 4)}{2} > \frac{- 8}{2}$ or $- 3 x + 4 > x - 4$

Divide $x + 4$ by $1$ .

$x + 4 > \frac{- 8}{2}$ or $- 3 x + 4 > x - 4$

Simplify the right side.

Divide $- 8$ by $2$ .

$x + 4 > - 4$ or $- 3 x + 4 > x - 4$

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

Subtract $4$ from both sides of the inequality.

$x > - 4 - 4$ or $- 3 x + 4 > x - 4$

Subtract $4$ from $- 4$ .

$x > - 8$ or $- 3 x + 4 > x - 4$

Step 2

Simplify the second inequality.

Move all terms containing $x$ to the left side of the inequality.

Subtract $x$ from both sides of the inequality.

$x > - 8$ or $- 3 x + 4 - x > - 4$

Subtract $x$ from $- 3 x$ .

$x > - 8$ or $- 4 x + 4 > - 4$

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

Subtract $4$ from both sides of the inequality.

$x > - 8$ or $- 4 x > - 4 - 4$

Subtract $4$ from $- 4$ .

$x > - 8$ or $- 4 x > - 8$

Divide each term in $- 4 x > - 8$ by $- 4$ and simplify.

Divide each term in $- 4 x > - 8$ by $- 4$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$x > - 8$ or $\frac{- 4 x}{- 4} < \frac{- 8}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$x > - 8$ or $\frac{- 4 x}{- 4} < \frac{- 8}{- 4}$

Divide $x$ by $1$ .

$x > - 8$ or $x < \frac{- 8}{- 4}$

Simplify the right side.

Divide $- 8$ by $- 4$ .

$x > - 8$ or $x < 2$

Step 3

The union consists of all of the elements that are contained in each interval.

All real numbers

Step 4

The result can be shown in multiple forms.

All real numbers

Interval Notation:

$(- \infty, \infty)$

Step 5

Solve the System of Inequalities -8<2(x+4) or -3x+4>x-4

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