Problem Solving

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

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