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23 Apr 2024, 07:19
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B
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If \(|p – |p|| = 3\), how many values of \(p\) satisfy this equation?
A. 0
B. 1
C. 2
D. 3
E. 4
A. 0
B. 1
C. 2
D. 3
E. 4
23 Apr 2024, 07:19
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Official Solution:
If \(|p – |p|| = 3\), how many values of \(p\) satisfy this equation?
A. 0
B. 1
C. 2
D. 3
E. 4
When \(p \geq 0\), then \(|p| = p\), so in this case we'd have \(|p - p| = 3\), which gives \(0 = 3\). This is obviously incorrect. Therefore, \(p\) cannot be 0 or positive.
Thus, \(p < 0\). In this case, \(|p| = -p\), so we'd have \(|p + p| = 3\), which gives \(|2p| = 3\). This simplifies to \(p = -\frac{3}{2}\) (since \(p = \frac{3}{2}\) is not possible because we know that \(p\) is negative). Therefore, one value of \(p\) satisfies the given equation.
Answer: B
If \(|p – |p|| = 3\), how many values of \(p\) satisfy this equation?
A. 0
B. 1
C. 2
D. 3
E. 4
When \(p \geq 0\), then \(|p| = p\), so in this case we'd have \(|p - p| = 3\), which gives \(0 = 3\). This is obviously incorrect. Therefore, \(p\) cannot be 0 or positive.
Thus, \(p < 0\). In this case, \(|p| = -p\), so we'd have \(|p + p| = 3\), which gives \(|2p| = 3\). This simplifies to \(p = -\frac{3}{2}\) (since \(p = \frac{3}{2}\) is not possible because we know that \(p\) is negative). Therefore, one value of \(p\) satisfies the given equation.
Answer: B
02 Jan 2025, 09:26
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In the second case, if |p|=-p then we should have |-p+p|=3 which will give us 0=3 "coz -p is already present in the equation"
Please let me know if I made a mistake?
Please let me know if I made a mistake?
