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

1 Answer
Nghi N
Jul 6, 2017

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

Explanation:

Solving by the double-number- line method.
First solve foe x in the 2 inequalities:
#2x - 2 <= 0# --> #2x <= 2# --> #x <= 1 # (1)
#2x + 5 > 15# --># 2x > 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)

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