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 |2x + 5| = |3x − 2|, which of the following is a possib
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If |x| = |y|, then either x = y OR x = -yVJesus12 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
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
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If the two expressions inside the absolute value signs are either both positive or both negative, we have: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
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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