# How do you solve the compound inequality 2x-2<=0 or 2x+5>15?

Jul 6, 2017

(-inf, 1] and (5, +inf)

#### Explanation:

Solving by the double-number- line method.
First solve foe x in the 2 inequalities:
$2 x - 2 \le 0$ --> $2 x \le 2$ --> $x \le 1$ (1)
$2 x + 5 > 15$ -->$2 x > 10$ --> $x > 5$ (2)

Mark these values of x on a double-number-line:

(1) + + + + + + + + + +1 - - - - - - - - - - - - 5 - - - - - - - - - - - -- -
(2) - - - - - - - - - - - - -1 - - - - - - - - - - - - 5 + + + + + + + + + +

By superimposing, the compound solution set are:
half closed interval (- inf, 1] and open interval (5, inf)