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27 Jan 2024, 05:01
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C
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- \(\frac{1}{3 - \frac{6}{x - 4}}\)
The expression above is defined for which of the following values of x?
I. x = 4
II. x = 6
III. x = 8
A. I only
B. II only
C. III only
D. II and III only
E. I, II, and III
Attachment:
2024-01-27_15-54-59.png [ 28.03 KiB | Viewed 5138 times ]
27 Jan 2024, 05:05
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guddo
- \(\frac{1}{3 - \frac{6}{x - 4}}\)
The expression above is defined for which of the following values of x?
I. x = 4
II. x = 6
III. x = 8
A. I only
B. II only
C. III only
D. II and III only
E. I, II, and III
Attachment:
2024-01-27_15-54-59.png
For the given expression to be defined, the denominators must not be zero.
Therefore, x - 4 should not equal 0, implying that x cannot be 4.
Similarly, 3 - 6/(x - 4) must not equal 0, meaning 6/(x - 4) should not equal 3. From this, it follows that (x - 4) must not equal 2, and therefore, x cannot be 6.
Answer: C.
27 Jan 2024, 13:07
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guddo
- \(\frac{1}{3 - \frac{6}{x - 4}}\)
The expression above is defined for which of the following values of x?
I. x = 4
II. x = 6
III. x = 8
A. I only
B. II only
C. III only
D. II and III only
E. I, II, and III
Attachment:
2024-01-27_15-54-59.png
The denominator should not be equal to zero, therefore \(x \neq 4\)
\(\frac{1}{3 - \frac{6}{x - 4}}\)
\(\frac{1}{\frac{3(x-4) - 6}{x-4}}\)
\(\frac{x-4}{3(x-4) - 6}\)
\(\frac{x-4}{3x-18}\)
\(3x-18 \neq 0\)
\(x \neq \frac{18}{3}\)
\(x \neq 6\)
Therefore, x cannot be 4 or 6. It can be any other value such as 8.
Option C
