Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus

Difference between revisions of "1962 AHSME Problems/Problem 33"

(→‎Solution)
 
Line 10: Line 10:
  
 
==Solution==
 
==Solution==
−
{{solution}}
+
This inequality can be split into two inequalities:
 +
<math>2\le x-1\le5</math> or <math>2\le1-x\le5</math>. Solving for x gives
 +
<math>3\le x\le6</math> or <math>-4\le x\le-1</math>. <math>\boxed{\textbf{(A)}}</math>

Latest revision as of 17:45, 17 April 2014

Problem

The set of $x$-values satisfying the inequality $2 \leq |x-1| \leq 5$ is:

$\textbf{(A)}\ -4\leq x\leq-1\text{ or }3\leq x\leq 6\qquad$

$\textbf{(B)}\ 3\leq x\leq 6\text{ or }-6\leq x\leq-3\qquad\textbf{(C)}\ x\leq-1\text{ or }x\geq 3\qquad$

$\textbf{(D)}\ -1\leq x\leq 3\qquad\textbf{(E)}\ -4\leq x\leq 6$


Solution

This inequality can be split into two inequalities: $2\le x-1\le5$ or $2\le1-x\le5$. Solving for x gives $3\le x\le6$ or $-4\le x\le-1$. $\boxed{\textbf{(A)}}$

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=1962_AHSME_Problems/Problem_33&oldid=61497"