What is the range of the solutions to the equation $|2x - 3| = 7?$ - The Beat The GMAT Forum

What is the range of the solutions to the equation $|2x - 3| = 7?$

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Vincen: Legendary Member; Posts: 2898; Joined: Thu Sep 07, 2017 2:49 pmFollowed by: 5 members; Thanked: 6 times

by Vincen » Tue Oct 06, 2020 7:15 am

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What is the range of the solutions to the equation $|2x - 3| = 7?$

A. 4
B. 5
C. 6
D. 7
E. 8

Answer: D

Source: Veritas Prep

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Source: Beat The GMAT — Problem Solving | Tue Oct 06, 2020 7:15 am

ashwinkohli: Junior | Next Rank: 30 Posts; Posts: 18; Joined: Thu Oct 01, 2020 8:55 am

Re: What is the range of the solutions to the equation $|2x - 3| = 7?$

by ashwinkohli » Tue Oct 06, 2020 10:22 am

Case 1: 2x-3=7

2x=10 and x=5

Case 2: 2x-3=-7

2x=-4, x=-2

Range is 5-(-2) = 7

hence D

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8155; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

Re: What is the range of the solutions to the equation $|2x - 3| = 7?$

by Scott@TargetTestPrep » Sat Oct 10, 2020 2:27 pm

Vincen wrote: ↑
Tue Oct 06, 2020 7:15 am
What is the range of the solutions to the equation $|2x - 3| = 7?$

A. 4
B. 5
C. 6
D. 7
E. 8

Answer: D

Solution:

Since |7| = |-7| = 7, we see that 2x - 3 = 7 or 2x - 3 = -7. If it’s the former, we have 2x = 10 → x = 5. If it’s the latter, we have: 2x = -4 → x = -2. Therefore, the range of solutions is 5 - (-2) = 7.

Answer: D

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