If x ≡ 4 (mod 7), which of the following could be a possible value of x?

₹0.0

Question: If x ≡ 4 (mod 7), which of the following could be a possible value of x?

Options:

Correct Answer: 11

Solution:

11 mod 7 = 4, so x could be 11.

If x ≡ 4 (mod 7), which of the following could be a possible value of x?

If x ≡ 4 (mod 7), which of the following could be a possible value of x?

Step 1: Understand what 'x ≡ 4 (mod 7)' means. This means that when x is divided by 7, the remainder is 4.
Step 2: Find numbers that give a remainder of 4 when divided by 7. Start with 4 itself, since 4 mod 7 = 4.
Step 3: Add 7 to 4 to find another possible value: 4 + 7 = 11. Check: 11 mod 7 = 4, so 11 is a valid option.
Step 4: You can also subtract 7 from 4 to find another possible value: 4 - 7 = -3. Check: -3 mod 7 = 4, so -3 is also valid.
Step 5: Continue this process to find more values: 4 + 14 = 18, and check: 18 mod 7 = 4, so 18 is valid too.

Modular Arithmetic – Understanding congruences and how to find equivalent values under a modulus.