Answer to Question #347917 in Algebra for Dhruv bartwal

Question #347917

Show that if 5/3< 2x< 11/3, then x∈{y∈R such that |y- 4/3| < 1/2}

1
Expert's answer
2022-06-06T14:27:28-0400
53<2x<113\dfrac{5}{3}<2x<\dfrac{11}{3}

56<x<116\dfrac{5}{6}<x<\dfrac{11}{6}

5643<x43<11643\dfrac{5}{6}-\dfrac{4}{3}<x-\dfrac{4}{3}<\dfrac{11}{6}-\dfrac{4}{3}

12<x43<12-\dfrac{1}{2}<x-\dfrac{4}{3}<\dfrac{1}{2}

Therefore if 53<2x<113,\dfrac{5}{3}<2x<\dfrac{11}{3}, then x43<12.|x-\dfrac{4}{3}|<\dfrac{1}{2}.



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