Question : If $x$ is prime number and $-1 \leq \frac{2x-7}{5} \leq 1$, then the number of values of $x$ is:
Option 1: 4
Option 2: 3
Option 3: 2
Option 4: 5
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Correct Answer: 3
Solution :
Given:
$x$ is prime number and $-1 \leq \frac{2x-7}{5} \leq 1$.
So, $-1 \leq \frac{2x-7}{5}$
$⇒-5 \leq 2x-7$
So, $1 \leq x$
Again, $\frac{2x-7}{5} \leq 1$
$⇒2x-7 \leq 5$
$\therefore x \leq 6$
Therefore, values of $x$ are 2, 3, and 5. [as $x$ is a prime number]
Hence, the correct answer is 3.
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