LINR 2 | Lesson 1 | Explore Absolute Value Solutions

  1.  Since \(|x | = 5\) means that the distance of \(x\) is 5 units from zero, then \(x=-5\) and \(x= 5\).
  2. Since \(|x – 3| = 5\)  means that the quantity of \((x – 3) \) is 5 units from zero, then \((x-3)= 5\) or \((x – 3) = -5\). Solving each equation, we find that \(x = 8\) or \(x = -2\)
  3. \(|2x – 3| = 5\) means that \((2x – 3 )= 5 \) or \((2x – 3) = -5\). Solving each equation, we find that \(x = 4\) or \(x = -1\)
  4. \(|x | = -5\) means that the distance from zero is -5, but distance is always positive therefore there is no solution.

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