MathDB
Absolute value equation

Source: 1959 AHSME Problem 25

August 14, 2013
inequalitiesAMCabsolute valueInequalityAMC 12

Problem Statement

The symbol a|a| means +a+a if aa is greater than or equal to zero, and a-a if aa is less than or equal to zero; the symbol << means "less than"; the symbol >> means "greater than." The set of values xx satisfying the inequality 3x<4|3-x|<4 consists of all xx such that: <spanclass=latexbold>(A)</span> x2<49<spanclass=latexbold>(B)</span> x2>1<spanclass=latexbold>(C)</span> 1<x2<49<spanclass=latexbold>(D)</span> 1<x<7<spanclass=latexbold>(E)</span> 7<x<1 <span class='latex-bold'>(A)</span>\ x^2<49 \qquad<span class='latex-bold'>(B)</span>\ x^2>1 \qquad<span class='latex-bold'>(C)</span>\ 1<x^2<49\qquad<span class='latex-bold'>(D)</span>\ -1<x<7\qquad<span class='latex-bold'>(E)</span>\ -7<x<1