SOLUTION: What is the solution set of y^2 - 2y ≤ 3y + 14? (A) y ≥ -2 (B) y ≤ 7 (C) y ≤ -2 or y ≥ 7 (D) -7 ≤ y ≤ 2 (E) -2 ≤ y ≤ 7

Algebra ->  Inequalities -> SOLUTION: What is the solution set of y^2 - 2y ≤ 3y + 14? (A) y ≥ -2 (B) y ≤ 7 (C) y ≤ -2 or y ≥ 7 (D) -7 ≤ y ≤ 2 (E) -2 ≤ y ≤ 7      Log On


   

Question 329596: What is the solution set of y^2 - 2y ≤ 3y + 14?
(A) y ≥ -2
(B) y ≤ 7
(C) y ≤ -2 or y ≥ 7
(D) -7 ≤ y ≤ 2
(E) -2 ≤ y ≤ 7
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
y%5E2-+2y+%3C=3y+%2B+14
y%5E2-+5y+-14%3C=0
%28y-7%29%28y%2B2%29%3C=0
Break up the number line into 3 regions.
Region 1:( -infinity,-2)
Region 2:(-2,7)
Region 3:(7, infinity)
.
.
Choose a point in the region and test the inequality.
Region 1: x=-3
%28-3-7%29%28-3%2B2%29%3C=0
%28-10%29%28-1%29%3C=0
10%3C=0
False, this region is not part of the solution.
.
.
Region 2: x=0
%280-7%29%280%2B2%29%3C=0
%28-7%29%282%29%3C=0
-14%3C=0
True, this region is part of the solution.
.
.
Region 3: x=8
%288-7%29%287%2B2%29%3C=0
%281%29%289%29%3C=0
9%3C=0
False, this region is not part of the solution.
.
.
The solution region is Region 2.
E) is the correct answer.