Unions and Intrsections

Question

Solve the compound inequality and give your answer in interval notation.

−2x+3 > −3x+10 AND 3(−5x+2)+3 ≥ −6x−63

Answer 1

The solution above is correct EXCEPT that it is not in interval notation. The intersection of the solution sets is 7 < x =< 8. In interval notation, this is (7,8].

Answer 2

-2x + 3 > -3x + 10 AND 3(-5x + 2) + 3 ≥ - 6x - 63

+ 3x + 3x - 3 - 3

x + 3 > 10 3(-5x + 2) ≥ - 6x - 66

-3 -3 - 5x + 2 ≥ - 2x - 22

x > 7 + 2x + 2x

-3x + 2 ≥ - 22

-2 -2

-3x ≥ -24

x ≤ 8

7 < x ≤ 8