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If (x – 3)(x + 2) = (x – 2)(x + 3), then x =
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18 Apr 2018, 11:58
18 Apr 2018, 11:58
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96% (00:56) correct
3% (03:27) wrong based on 55 sessions
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If (x – 3)(x + 2) = (x – 2)(x + 3), then x =
(A) –3
(B) –2
(C) 0
(D) 2
(E) 3
(A) –3
(B) –2
(C) 0
(D) 2
(E) 3
Re: If (x – 3)(x + 2) = (x – 2)(x + 3), then x =
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18 Apr 2018, 21:14
18 Apr 2018, 21:14
1
Use foil to expand the equation on both sides
\(x^2 + 2x -3x - 6 = x^2 +3x -2x -6\)
\(x^2\) and \(-6\) cancels out so the eqn reduces to
\(2x - 3x = 3x -2x\)
Hence, \(-x = x\)
This situation is satisfied only if \(x = 0\)
option c
\(x^2 + 2x -3x - 6 = x^2 +3x -2x -6\)
\(x^2\) and \(-6\) cancels out so the eqn reduces to
\(2x - 3x = 3x -2x\)
Hence, \(-x = x\)
This situation is satisfied only if \(x = 0\)
option c
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If (x – 3)(x + 2) = (x – 2)(x + 3), then x =
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08 Feb 2021, 15:13
08 Feb 2021, 15:13
1
Carcass wrote:
If (x – 3)(x + 2) = (x – 2)(x + 3), then x =
(A) –3
(B) –2
(C) 0
(D) 2
(E) 3
(A) –3
(B) –2
(C) 0
(D) 2
(E) 3
Great question!
I love that we can eliminate 4 answer choices by inspection.
For example, if x = 3 (answer choice E), then we can see that we get: (3 – 3)(3 + 2) = (3 – 2)(3 + 3)
Simplify (in head) to get: (ZERO)(non-zero #) = (non-zero #)(non-zero #)
This equation cannot hold true. So ELIMINATE E
Using the same logic we can also ELIMINATE A, B and D, which leaves us with C, the correct answer.
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The LONGER approach is to EXPAND and SOLVE
Given: (x – 3)(x + 2) = (x – 2)(x + 3)
Expand and simplify: x² - x - 6 = x² + x - 6
Add 6 to both sides to get: x² - x = x² + x
Subtract x² from both sides to get: -x = x
Add x to both sides: 0 = 2x
Solve: x = 0
Answer: C
