Question

For which value of x is the value of the expression $7x+1$a prime number?

A. $0$

B. $1$

C. $3$

D. $4$

Short answer

The correction is D which is $4$.

Step-by-step solution

Step 1. Apply the concept of prime number 

In this, simply use the concept of prime number which means a number who has two factors $1$ and the number itself.

Step 2. Put the different values in the equation 

Here, the equation is $7x+1$.

A. Put $x=0$ in the above equation,

$\begin{array}{l}=7x+1\\ =7\left(0\right)+1\\ =0+1\\ =1\end{array}$

$1$ is not a prime number.

B. Put $x=1$ in the above equation,

$\begin{array}{l}=7x+1\\ =7\left(1\right)+1\\ =7+1\\ =8\end{array}$

$8$ is not a prime number.

C. Put $x=3$ in the above equation,

$\begin{array}{l}=7x+1\\ =7\left(3\right)+1\\ =21+1\\ =22\end{array}$

$22$ is not a prime number.

D. Put $x=4$ in the above equation,

$\begin{array}{l}=7x+1\\ =7\left(4\right)+1\\ =28+1\\ =29\end{array}$

$29$ is a prime number.

Step 3. Eliminating the other options to get the correct one

A. $0$: It is the incorrect option because after putting it gives $1$ which is not prime.

B. $1$: It is the correct option because after putting it gives $8$ which is not prime.

C. $3$: It is the incorrect option because after putting it gives $22$ which is not prime.

D. $4$: It is the correct option because after putting it gives $29$ which is prime.