If |2x + 5| = |3x âˆ’ 2|, which of the following is a possib

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VJesus12: Legendary Member; Posts: 2276; Joined: Sat Oct 14, 2017 6:10 am; Followed by:3 members

If |2x + 5| = |3x âˆ’ 2|, which of the following is a possib

by VJesus12 » Mon Jun 17, 2019 4:14 am

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If |2x + 5| = |3x âˆ’ 2|, which of the following is a possible value of x?

(a) -7
(b) -19/5
(c) -3/5
(d) 3/5
(e) 5

[spoiler]OA=C[/spoiler]

Source: Veritas Prep

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Source: Beat The GMAT — Problem Solving | Mon Jun 17, 2019 4:14 am

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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 » Mon Jun 17, 2019 4:35 am

VJesus12 wrote:If |2x + 5| = |3x âˆ’ 2|, which of the following is a possible value of x?

(a) -7
(b) -19/5
(c) -3/5
(d) 3/5
(e) 5

[spoiler]OA=C[/spoiler]

Source: Veritas Prep

If |x| = |y|, then either x = y OR x = -y

GIVEN: |2x + 5| = |3x âˆ’ 2|
So, EITHER 2x + 5 = 3x âˆ’ 2 OR 2x + 5 = -(3x âˆ’ 2)

Let's solve each equation...
Take: 2x + 5 = 3x âˆ’ 2
We get: 5 = x - 2
Solve: x = 7
Check answer choices.....x = 7 is not there.

Try the other equation:
Take: 2x + 5 = -(3x âˆ’ 2)
Simplify: 2x + 5 = -3x + 2
Add 3x to both sides: 5x + 5 = 2
So: 5x = -3
Solve: x = -3/5

Answer: C

Cheers,
Brent

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 » Wed Jun 19, 2019 5:43 pm

VJesus12 wrote:If |2x + 5| = |3x âˆ’ 2|, which of the following is a possible value of x?

(a) -7
(b) -19/5
(c) -3/5
(d) 3/5
(e) 5

[spoiler]OA=C[/spoiler]

Source: Veritas Prep

If the two expressions inside the absolute value signs are either both positive or both negative, we have:

2x + 5 = 3x - 2

7 = x

However, 7 is not in the answer choices.

Next, if the two expressions inside the absolute value signs have opposite signs (i.e., one is positive and the other is negative, or vice versa), we have:

2x + 5 = -(3x - 2)

2x + 5 = -3x + 2

5x = -3

x = -3/5

Answer: C

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