Recording-2025-01-09T18:37:46.324Z

Understanding Absolute Value

• Definition: Absolute value represents the distance of a number from 0 on a number line.

Evaluating Absolute Values

• Absolute Value of 3:

  • Find 3 on the number line.

  • Distance from 0: 1, 2, 3 units.

  • Therefore, |3| = 3.

• Absolute Value of -3:

  • Find -3 on the number line.

  • Distance from 0: 1, 2, 3 units.

  • Therefore, |-3| = 3.

Negative of Absolute Values

• Negative of the Absolute Value of 3:

  • Since |3| = 3, the negative is -3.

• Negative of the Absolute Value of -3:

  • Since |-3| = 3, the negative is -3.

Solving Equations Without Absolute Values

• Equation: x = 1.5:

  • Plotted at 1.5 on the number line.

• Equation: -x = 1.5:

  • Isolate x: Divide by -1 gives x = -1.5.

  • Plotted at -1.5 on the number line.

Solving Equations With Absolute Values

• Equation: |x| = 1.5:

  • Distance from 0 can be positive or negative.

  • Two solutions: x = 1.5 or x = -1.5.

Example of Negative x with Absolute Value

• Equation: |-x| = 1.5:

  • The absolute value remains the same.

  • Two cases: -x = 1.5 or -x = -1.5.

  • Isolate x:

    • For -x = 1.5, x = -1.5.

    • For -x = -1.5, x = 1.5.

Summary of Solutions

• For equations with or without absolute values, consistent results yield solutions:

  • x = 1.5 or x = -1.5.

Transition to Next Example

• Ready to explore more complex examples involving absolute values.