Algebra Practice Test 2025 – Complete Exam Preparation

Question: 1 / 400

What is the solution set for the equation |x| = 5?

{5}

{-5}

{5, -5}

The equation |x| = 5 represents the absolute value, which measures the distance of a number from zero on the number line. This distance can be positive or negative, as absolute value does not concern itself with direction. Consequently, the equation |x| = 5 implies that there are two scenarios for the value of x:

1. When x is equal to 5, which directly satisfies the equation since the distance from zero is indeed 5.

2. When x is equal to -5, as the distance from zero is also 5 in this case, but in the negative direction.

Thus, the solution set includes both values: 5 and -5. Therefore, the complete solution set for the equation |x| = 5 is {5, -5}, demonstrating that both positive and negative values are valid solutions based on the definition of absolute value.

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