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Absolute value equation

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Algebra and Trigonometry

Definition

An absolute value equation is an equation that contains an absolute value expression, which represents the distance of a number from zero on the number line. Solutions are obtained by considering both the positive and negative scenarios of the expression inside the absolute value.

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5 Must Know Facts For Your Next Test

  1. Absolute value equations have two cases: one for the positive value and one for the negative value of the expression within the absolute value.
  2. The basic form of an absolute value equation is $|ax + b| = c$, where $c$ is a non-negative constant.
  3. To solve $|ax + b| = c$, you must split it into two separate linear equations: $ax + b = c$ and $ax + b = -c$.
  4. If $c < 0$, then $|ax + b| = c$ has no solution, because absolute values cannot be negative.
  5. Always check your solutions in the original equation, as extraneous solutions can arise during solving.

Review Questions

  • What are the two cases you need to consider when solving an absolute value equation?
  • How do you solve $|3x - 4| = 5$?
  • What does it mean if you encounter a negative constant on the right side of an absolute value equation?

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