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Absolute Values

Source: 1964 AHSME Problem 27

August 23, 2013
inequalitiesAMC

Problem Statement

If xx is a real number and ∣x−4∣+∣x−3∣<a|x-4|+|x-3|<a where a>0a>0, then:
<spanclass=′latex−bold′>(A)</span> 0<a<.01<spanclass=′latex−bold′>(B)</span> .01<a<1<spanclass=′latex−bold′>(C)</span> 0<a<1 <span class='latex-bold'>(A)</span>\ 0<a<.01\qquad<span class='latex-bold'>(B)</span>\ .01<a<1 \qquad<span class='latex-bold'>(C)</span>\ 0<a<1\qquad
<spanclass=′latex−bold′>(D)</span> 0<a≤1<spanclass=′latex−bold′>(E)</span> a>1<span class='latex-bold'>(D)</span>\ 0<a \le 1\qquad<span class='latex-bold'>(E)</span>\ a>1
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