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

(A) x > 3
(B) x ≤ 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

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

(A) x > 3
(B) x ≤ 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