Inequalities/Algebra

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BTGmoderatorRO: Moderator; Posts: 772; Joined: Wed Aug 30, 2017 6:29 pm; Followed by:6 members

Inequalities/Algebra

by BTGmoderatorRO » Sun Nov 19, 2017 1:25 pm

If |x-1|<4, so:

(A) x > 3
(B) x â‰¤ 4
(C) -4< x < 4
(D) x > -4
(E) none of the above
OA is d

what mathematical approach can i use to solve this question? can any expert help me?
Thanks so much for your help

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Source: Beat The GMAT — Problem Solving | Sun Nov 19, 2017 1:25 pm

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pm; Location: Vancouver, BC; Thanked: 5254 times; Followed by:1268 members; GMAT Score:770

by Brent@GMATPrepNow » Sun Nov 19, 2017 1:54 pm

Roland2rule wrote:If |x - 1| < 4, so:

(A) x > 3
(B) x â‰¤ 4
(C) -4< x < 4
(D) x > -4
(E) none of the above

When solving inequalities involving ABSOLUTE VALUE, there are 2 things you need to know:
Rule #1: If |something| < k, then -k < something < k
Rule #2: If |something| > k, then EITHER something > k OR something < -k
Note: these rules assume that k is positive

Given: |x - 1| < 4
Apply rule #1 to get: -4 < x - 1 < 4
Add 1 to all sides to get: -3 < x < 5

NOTE: none of the answer choices match -3 < x < 5
However, if -3 < x < 5, then we can be certain that x is greater than -4
So, even though answer choice D doesn't list all of the possible values of x (as does the inequality -3 < x < 5), we can still say that answer choice D is true.

Answer: D

Brent Hanneson - Creator of GMATPrepNow.com

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Thu Oct 17, 2019 7:25 pm

BTGmoderatorRO wrote:If |x-1|<4, so:

(A) x > 3
(B) x â‰¤ 4
(C) -4< x < 4
(D) x > -4
(E) none of the above
OA is d

what mathematical approach can i use to solve this question? can any expert help me?
Thanks so much for your help

If |x - 1| < 4, then:

-4 < x - 1 < 4

-3 < x < 5

We see that the correct solution is -3 < x < 5. However, since this interval contains all the values that are greater than -4, D is the correct answer.

(Note: In general, this is not a good problem when you also have choice E; some people would argue that choice E should be correct choice since the actual solution is -3 < x < 5.)

Answer: D

Scott Woodbury-Stewart
Founder and CEO
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