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If x is an integer such that |x + 1| < 2, which of the following is a
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01 Mar 2022, 04:00
01 Mar 2022, 04:00
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If x is an integer such that \(|x + 1| < 2\), which of the following is a possible value of \(2x^2 – 5x + 3\)?
Indicate all such values.
(A) 0
(B) 1
(C) 3
(D) 10
(E) 21
(F) 36
Indicate all such values.
(A) 0
(B) 1
(C) 3
(D) 10
(E) 21
(F) 36
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If x is an integer such that |x + 1| < 2, which of the following is a
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01 Mar 2022, 06:20
01 Mar 2022, 06:20
1
Carcass wrote:
If x is an integer such that \(|x + 1| < 2\), which of the following is a possible value of \(2x^2 – 5x + 3\)?
Indicate all such values.
(A) 0
(B) 1
(C) 3
(D) 10
(E) 21
(F) 36
Indicate all such values.
(A) 0
(B) 1
(C) 3
(D) 10
(E) 21
(F) 36
Two properties involving absolute value inequalities:
Property #1: If |something| < k, then –k < something < k
Property #2: If |something| > k, then EITHER something > k OR something < -k
Note: these rules assume that k is positive
Since the given inequality, \(|x + 1| < 2\), is in the same form as property #1, we can write: \( -2 < x + 1 < 2\)
Subtract \(1\) from all sides of the inequality to get: : \( -3 < x < 1\)
Since \(x\) is an integer, there are only three possible values of x that satisfy the above inequality: \(x = -2\), \(x = -1\) and \(x = 0\)
So, to find the possible values of \(2x^2 – 5x + 3\), we'll plug these possible x-values into the expression.
If \(x = -2\), then \(2x^2 – 5x + 3 = 2(-2)^2 – 5(-2) + 3 = 8 + 10 + 3 = 21\)
If \(x = -1\), then \(2x^2 – 5x + 3 = 2(-1)^2 – 5(-1) + 3 = 2 + 5 + 3 = 10\)
If \(x = 0\), then \(2x^2 – 5x + 3 = 2(0)^2 – 5(0) + 3 = 0 + 0 + 3 = 3\)
Answer: C, D and E
gmatclubot
If x is an integer such that |x + 1| < 2, which of the following is a [#permalink]
01 Mar 2022, 06:20
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