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If 2 < x < 5 and 7 < y < 10, then 1/(y - x) is between
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01 Mar 2022, 04:00
01 Mar 2022, 04:00
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Question Stats:
83% (01:13) correct
16% (02:19) wrong based on 6 sessions
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If \(2 < x < 5\) and \(7 < y < 10\), then \(\frac{1}{(y - x)}\) is between
(A) 1/8 and 1
(B) 1/4 and 1
(C) 1/5 and 2/3
(D) 1/8 and 1/2
(E) 1/2 and 2/3
(A) 1/8 and 1
(B) 1/4 and 1
(C) 1/5 and 2/3
(D) 1/8 and 1/2
(E) 1/2 and 2/3
Re: If 2 < x < 5 and 7 < y < 10, then 1/(y - x) is between
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01 Mar 2022, 07:33
01 Mar 2022, 07:33
1
\(2 < x < 5\) and \(7 < y < 10\)
Subtract \(x\) from \(y\)
\(7-5 < y-x < 10-2\)
\(2 < y - x < 8\)
Inversing the inequality, we will get
\(\frac{1}{2} > \frac{1}{y - x} > \frac{1}{8}\)
Answer \(D\)
Subtract \(x\) from \(y\)
\(7-5 < y-x < 10-2\)
\(2 < y - x < 8\)
Inversing the inequality, we will get
\(\frac{1}{2} > \frac{1}{y - x} > \frac{1}{8}\)
Answer \(D\)
Re: If 2 < x < 5 and 7 < y < 10, then 1/(y - x) is between
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01 Mar 2022, 14:03
01 Mar 2022, 14:03
1
Carcass wrote:
If \(2 < x < 5\) and \(7 < y < 10\), then \(\frac{1}{(y - x)}\) is between
(A) 1/8 and 1
(B) 1/4 and 1
(C) 1/5 and 2/3
(D) 1/8 and 1/2
(E) 1/2 and 2/3
(A) 1/8 and 1
(B) 1/4 and 1
(C) 1/5 and 2/3
(D) 1/8 and 1/2
(E) 1/2 and 2/3
The endpoints for y are 7 and 10.
The endpoints for x are 2 and 5.
To determine the range of y-x, calculate y-x using EVERY POSSIBLE COMBINATION OF ENDPOINTS:
7-2 = 5
7-5 = 2
10-2 = 8
10-5 = 5
The smallest result is 2, and the greatest result is 8.
Thus:
2 < y-x < 8
Implication:
The endpoints for \(\frac{1}{y-x}\) are \(\frac{1}{2}\) and \(\frac{1}{8}\)
Show: ::
D
