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Absolute Value Equations quiz

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  • What does the absolute value of a number represent?
    The absolute value represents the distance of a number from zero, which is always non-negative.
  • How do you solve an equation of the form |x| = a when a is positive?
    Rewrite it as two equations: x = a and x = -a, then solve both for x.
  • What is the solution to |x| = 2?
    The solutions are x = 2 and x = -2.
  • What is the first step when solving an absolute value equation?
    Isolate the absolute value expression on one side of the equation.
  • How do you solve |x + 1| = 2?
    Set x + 1 = 2 and x + 1 = -2, then solve to get x = 1 and x = -3.
  • What do you do if the absolute value equation is not isolated, such as |x + 1| + 3 = 5?
    Subtract 3 from both sides to isolate the absolute value, resulting in |x + 1| = 2.
  • What happens when you solve |x| = 0?
    Set x = 0, so the only solution is x = 0.
  • Why does |x| = -2 have no solution?
    Absolute value cannot be negative, so there are no values of x that satisfy the equation.
  • How many solutions does |x| = a have when a is negative?
    There are no solutions because absolute value cannot be negative.
  • What is the general rule for solving |expression| = a?
    Rewrite as two equations: expression = a and expression = -a, then solve both.
  • How do you solve an equation with two absolute values, like |x + 1| = |2x - 4|?
    Rewrite as two equations: x + 1 = 2x - 4 and x + 1 = -(2x - 4), then solve both.
  • What are the two equations formed from |x| = |y|?
    The equations are x = y and x = -y.
  • What is the solution set for |x + 1| = |2x - 4|?
    The solutions are x = 5 and x = 1.
  • What is the process for solving |x + 1| = |2x - 4| after forming the equations?
    Solve x + 1 = 2x - 4 and x + 1 = -(2x - 4) separately to find the values of x.
  • Why must the absolute value be isolated before applying the solving rule?
    The rule only works when the absolute value is by itself, so isolating it ensures correct application.