# SOLUTION: If 3 < x < 7 and 4 < y < 7, which of the following best describes the range of values of x- y ? (A) –4 < x - y < 3 (B) 0 < x – y < 4 (C) 3 < x- y < 4 (D) 3 < x - y <

Algebra ->  Algebra  -> Inequalities -> SOLUTION: If 3 < x < 7 and 4 < y < 7, which of the following best describes the range of values of x- y ? (A) –4 < x - y < 3 (B) 0 < x – y < 4 (C) 3 < x- y < 4 (D) 3 < x - y <       Log On

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 Question 336661: If 3 < x < 7 and 4 < y < 7, which of the following best describes the range of values of x- y ? (A) –4 < x - y < 3 (B) 0 < x – y < 4 (C) 3 < x- y < 4 (D) 3 < x - y < 7 (E) 4 < x – y < 7 Answer by Edwin McCravy(8909)   (Show Source): You can put this solution on YOUR website!```3 < x < 7 and 4 < y < 7 There is a rule of ADDING inequalities in the same order, that is if A < B < C and D < E < F, then A+D < B+E < C+F But there is NO rule for subtracting them! But all is not lost, for we can change the second inequality to involve -y instead of +y and then we can use the addition rule. 4 < y < 7 Multiply through by -1. This will change the direction of the inequalities: -4 > -y > -7 But then that can be written equivantly as: -7 < -y < -4. Now we can use the rule for adding inequalities in the same order: 3 < x < 7 -7 < -y < -4 ---------------- -4 < x-y < 3 This is choice A Edwin```