If a number x is congruent to 5 modulo 8, which of the following could be a poss

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Question: If a number x is congruent to 5 modulo 8, which of the following could be a possible value of x?

Options:

Correct Answer: 13

Solution:

x = 5 + 8k for some integer k. 13 is 5 + 8(1), so it is congruent to 5 modulo 8.

If a number x is congruent to 5 modulo 8, which of the following could be a possible value of x?

If a number x is congruent to 5 modulo 8, which of the following could be a possible value of x?

Step 1: Understand what 'congruent to 5 modulo 8' means. It means when you divide x by 8, the remainder is 5.
Step 2: Write the formula for x based on the congruence: x = 5 + 8k, where k is any integer (like 0, 1, -1, etc.).
Step 3: Calculate some possible values of x by substituting different integers for k. For example, if k = 0, then x = 5 + 8(0) = 5. If k = 1, then x = 5 + 8(1) = 13. If k = -1, then x = 5 + 8(-1) = -3.
Step 4: List the possible values of x you found: 5, 13, -3, etc.
Step 5: Check if any of the given options match the possible values you calculated.

Modular Arithmetic – Understanding congruences and how to express numbers in terms of a modulus.
Integer Solutions – Recognizing that congruences can have multiple integer solutions based on the modulus.