Questions: Find the real numbers that satisfy the equation below. x=40

Find the real numbers that satisfy the equation below. x=40
Transcript text: Find the real numbers that satisfy the equation below. \[ |x|=40 \]
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Solution

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Solution Steps

To solve the equation \(|x| = 40\), we need to find the values of \(x\) that make the absolute value of \(x\) equal to 40. The absolute value equation \(|x| = a\) has two solutions: \(x = a\) and \(x = -a\).

Step 1: Understand the Absolute Value Equation

The equation given is \(|x| = 40\). The absolute value of a number is its distance from zero on the number line, regardless of direction. Therefore, \(|x| = a\) implies two possible solutions: \(x = a\) and \(x = -a\).

Step 2: Apply the Absolute Value Property

For the equation \(|x| = 40\), we apply the property of absolute values:

  • \(x = 40\)
  • \(x = -40\)

Final Answer

The real numbers that satisfy the equation \(|x| = 40\) are: \[ \boxed{x = 40} \quad \text{and} \quad \boxed{x = -40} \]

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