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23 Apr 2024, 07:43
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If \(\frac{\sqrt{x^2}}{\sqrt[3]{x^3}}=-1\) and \(x \neq 0\), what is the value of \(\frac{2|x| + 6}{3 - x}\) ?
A. -2
B. 1
C. 2
D. 3
E. Cannot be determined from the given information
A. -2
B. 1
C. 2
D. 3
E. Cannot be determined from the given information
23 Apr 2024, 07:43
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Official Solution:
If \(\frac{\sqrt{x^2}}{\sqrt[3]{x^3}}=-1\) and \(x \neq 0\), what is the value of \(\frac{2|x| + 6}{3 - x}\) ?
A. -2
B. 1
C. 2
D. 3
E. Cannot be determined from the given information
\(\frac{\sqrt{x^2}}{\sqrt[3]{x^3}} = -1\) simplifies to \(\frac{|x|}{x} = -1\), which then yields \(|x| = -x\). This indicates that \(x\) must be negative. If \(x < 0\), then \(|x| = -x\), and thus we get \(\frac{-2x + 6}{3 - x} = \frac{2(3 - x)}{3 - x} = 2\).
Answer: C
If \(\frac{\sqrt{x^2}}{\sqrt[3]{x^3}}=-1\) and \(x \neq 0\), what is the value of \(\frac{2|x| + 6}{3 - x}\) ?
A. -2
B. 1
C. 2
D. 3
E. Cannot be determined from the given information
\(\frac{\sqrt{x^2}}{\sqrt[3]{x^3}} = -1\) simplifies to \(\frac{|x|}{x} = -1\), which then yields \(|x| = -x\). This indicates that \(x\) must be negative. If \(x < 0\), then \(|x| = -x\), and thus we get \(\frac{-2x + 6}{3 - x} = \frac{2(3 - x)}{3 - x} = 2\).
Answer: C
17 Mar 2025, 10:40
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Here since x is negative we get the expression as \frac{2|x| + 6}{3 - (- x)} = \frac{2|x| + 6}{3 + x} , right ?
Bunuel
