For what value(s) of x is |x| = 4 true?

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Understand the meaning of the absolute value function: \(|x|\) represents the distance of \(x\) from zero on the number line, and it is always non-negative.

Set up the equation given: \(|x| = 4\) means we are looking for all values of \(x\) whose distance from zero is 4.

Recall the definition of absolute value: \(|x| = a\) implies \(x = a\) or \(x = -a\) when \(a \geq 0\).

Apply this to our problem: since \(a = 4\), the solutions are \(x = 4\) or \(x = -4\).

Conclude that the values of \(x\) satisfying \(|x| = 4\) are \(x = 4\) and \(x = -4\).

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Absolute Value Definition

The absolute value of a number represents its distance from zero on the number line, regardless of direction. For any real number x, |x| is always non-negative. For example, |4| = 4 and |-4| = 4.

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Solving Absolute Value Equations

An equation involving absolute value, such as |x| = a, where a ≥ 0, has two solutions: x = a and x = -a. This is because both values have the same distance from zero, satisfying the absolute value condition.

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Properties of Real Numbers

Understanding that real numbers include both positive and negative values is essential. When solving |x| = 4, recognizing that x can be either positive 4 or negative 4 relies on this property of real numbers.

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