Question

How to put in the solutions for ∣x∣=−5?

A) No solution
B) x=−5
C) x=5
D) x=±5

Answer 1

The correct solution for the equation ∣x∣=−5 is (Option A) No solution.

Step-by-step explanation:

The absolute value ∣x∣ represents the distance of x from the origin on the number line. It is always non-negative, as distance cannot be negative. In the given equation ∣x∣=−5, we are asked to find a value for x that satisfies this equality. However, no real number x can have an absolute value of -5 because the absolute value is always non-negative (Option A).

To elaborate, the absolute value of any real number is either zero or positive. Therefore, the equation ∣x∣=−5 has no solution in the set of real numbers. Option A) No solution accurately captures this mathematical reality.

It's crucial to understand that absolute values represent distances and distances are non-negative. In this context, no real number can satisfy the equation where the absolute value is set equal to a negative value. Hence, the correct answer is A) No solution. This conclusion aligns with the mathematical principles governing absolute values and their properties.