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2010 AMC 10A Problem 11

Problem 11 of 25IntermediateAlgebra

The length of the interval of solutions of the inequality a≤2x+3≤ba \le 2x + 3 \le b is 10.10. What is b−a?b - a?

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Solution

Splitting the inequality into two of them and solving gives us a≤2x+3 a \le 2x + 3 x≥a−32 x \ge \dfrac{a - 3}{2} and 2x+3≤b 2x + 3 \le b x≤b−32. x \le \dfrac{b - 3}{2}. The range of the solutions is then b−32−a−32=10, \dfrac{b - 3}{2} - \dfrac{a - 3}{2} = 10, which then simplifying gives us (b−3)−(a−3)=20 (b - 3) - (a - 3) = 20 b−a=20. b - a = 20. Thus, D is the correct answer.
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Tagged: inequality · linear equation

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