Solve the System of Inequalities x-8<=-12 or 2>x-8

$x - 8 \leq - 12$ or $2 > x - 8$

Step 1

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

Add $8$ to both sides of the inequality.

$x \leq - 12 + 8$ or $2 > x - 8$

Add $- 12$ and $8$ .

$x \leq - 4$ or $2 > x - 8$

Step 2

Simplify the second inequality.

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

$x \leq - 4$ or $x - 8 < 2$

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

Add $8$ to both sides of the inequality.

$x \leq - 4$ or $x < 2 + 8$

Add $2$ and $8$ .

$x \leq - 4$ or $x < 10$

Step 3

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

$x < 10$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x < 10$

Interval Notation:

$(- \infty, 10)$

Step 5