Question 683354: Find the integer solutions to : | 2y - 5 | ≥ 9
A. {... -4, -3, -2} or {7, 8, 9 ...}
B. {... -5, -4, -3} or {8, 9, 10 ...}
C. {-2, -1, 0, 1, 2, 3, 4, 5, 6, 7}
D. {-1, 0, 1, 2, 3, 4, 5, 6}
Answer by fcabanski(1391)   (Show Source):
You can put this solution on YOUR website! Absolute value means the thing itself or the opposite (-1 times it). Rewrite the equation as two equations.
The thing itself: 2y-5 >=9 ---> 2y >= 14 ---> y >= 7. The problem is multiple choice. Eliminate all the answers that don't include that y >= 7. B is out because it doesn't include 7. C is out because it doesn't include values larger than 7. D is out because it doesn't include 7 or values larger than 7. The only answer remaining is A.
Let's check the opposite for practice - that would help if this weren't multiple choice.
-(2y-5)>= 9 ---> (divide both sides by -1. With inequalities, if dividing both sides by -1 you flip the inequality sign.) 2y-5 <= -9 ---> 2y <= -4 ---> y <= -2. Answer A, in fact, does include all values less than or equal to -2.
Hope the solution helped. Sometimes you need more than a solution. Contact fcabanski@hotmail.com for online, private tutoring, or personalized problem solving (quick for groups of problems.)
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