What is the complete solution set for the inequality |x – 3| 4 ?

Question

What is the complete solution set for the inequality |x – 3| > 4 ? (A) x > –1 (B) x > 7 (C) –1 < x < 7 (D) x < –7, x > 7 (E) x < –1, x > 7

imeanup · Answer

Upon drawing the graph for the equation, we have  x < (-1)  and   x > 7   has positive values.  -1 < x < 7  has negative values.
 Ans E

erv20 · Answer

Hey could you please provide the graph of the equation? Also..If possible explain how you put it into a graph...

BrushMyQuant · Answer

|x – 3| > 4

We will have to take two cases

Case 1: Whatever is inside the modulus is >= 0
=> x-3 >= 0 => x >= 3
=> |x-3| = x-3 (as |X| = X when X >= 0)
=> x-3 > 4
=> x > 4+3
=> x > 7
7 >= 3
=> x > 7 is a solution

Case 2: Whatever is inside the modulus is < 0
=> x-3 < 0 => x < 3
=> |x-3| = -(x-3) (as |X| = -X when X < 0)
=> -(x-3) > 4
=> -x + 3 > 4
=> -x > 4-3
=> -x > 1
=> x < -1 (multiplying both the sides with -1 will reverse the sign of the inequality)
=> The condition was x < 3
-1 < 3
=> x < -1 is a solution

So, solution is x < -1 and x > 7

So, Answer will be E
Hope it helps!

Watch the following video to learn how to Solve Inequality + Absolute value Problems

What is the complete solution set for the inequality |x – 3| > 4 ?

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions