Will has a bag of gumdrops. If he eats 2 of his gumdrops, he will have among 2 and 6 of them left. Which of the subsequent represents how many gumdrops, x, were originally in his bag?
This problem is an instance of a compound inequality, where there is more than one inequality in the question. In order to solve it, let x = the total amount of gumdrops Will has. Set up the compound inequality, and then solve it as two separate inequalities. Thus, the second sentence in the problem could be written as: 2 < x - 2 < 6. The two inequalities are: 2 < x - 2 and x - 2 < 6. Add 2 to both sides of both inequalities: 2 + 2 < x - 2 + 2 and x - 2 + 2 < 6 + 2; simplify: 4 < x and x < 8. If x is greater than four and less than eight, it means that the solution is among 4 and 8. This can be shortened to: 4 < x < 8.