Solve the System of Inequalities 2x-4>-14 or 2x-4<=10

$2 x - 4 > - 14$ or $2 x - 4 \leq 10$

Simplify the first inequality.

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

Add $4$ to both sides of the inequality.

$2 x > - 14 + 4$ or $2 x - 4 \leq 10$

Add $- 14$ and $4$ .

$2 x > - 10$ or $2 x - 4 \leq 10$

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 $2 x - 4 \leq 10$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} > \frac{- 10}{2}$ or $2 x - 4 \leq 10$

Divide $x$ by $1$ .

$x > \frac{- 10}{2}$ or $2 x - 4 \leq 10$

Simplify the right side.

Divide $- 10$ by $2$ .

$x > - 5$ or $2 x - 4 \leq 10$

Simplify the second inequality.

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

Add $4$ to both sides of the inequality.

$x > - 5$ or $2 x \leq 10 + 4$

Add $10$ and $4$ .

$x > - 5$ or $2 x \leq 14$

Divide each term in $2 x \leq 14$ by $2$ and simplify.

Divide each term in $2 x \leq 14$ by $2$ .

$x > - 5$ or $\frac{2 x}{2} \leq \frac{14}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$x > - 5$ or $\frac{2 x}{2} \leq \frac{14}{2}$

Divide $x$ by $1$ .

$x > - 5$ or $x \leq \frac{14}{2}$

Simplify the right side.

Divide $14$ by $2$ .

$x > - 5$ or $x \leq 7$

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

All real numbers

The result can be shown in multiple forms.

All real numbers

Interval Notation:

$(- \infty, \infty)$