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

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

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If |2x + 5| = |3x − 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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by Brent@GMATPrepNow » Mon Jun 17, 2019 4:35 am
VJesus12 wrote:If |2x + 5| = |3x − 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 − 2|
So, EITHER 2x + 5 = 3x − 2 OR 2x + 5 = -(3x − 2)

Let's solve each equation...
Take: 2x + 5 = 3x − 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 − 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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by Scott@TargetTestPrep » Wed Jun 19, 2019 5:43 pm
VJesus12 wrote:If |2x + 5| = |3x − 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

Scott Woodbury-Stewart
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