Absolute Value Inequalities - PowerPoint by cbtms2B9

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									     Absolute Value Equalities and
             Inequalities
• Absolute value: The distance from zero on the
  number line.
• Example: The absolute value of 7, written as
  |7|, = 7
• The absolute value of – 3, written as | -3 |,
  = 3.
• An absolute value is never negative
      Solve | x | = 13. Note. There will
         generally be two answers.
                                Then, negate the right side of the
First, solve for the positive   inequality to find the second solution.
• X = 13                        • X = - 13
                  Solve |x – 3| = 6
                                Then, solve for the negative to
First, solve for the positive   find the second solution.
• X–3=6                         • X – 3 = -6
• X=9                           • X = -3
           Solve 2 + | x | = 20
• Treat the absolute value symbol as a grouping
  symbol. You must absolutely get the absolute
  value symbol by itself prior to solving the
  equation.
• 2 + | x| = 20
• | x| = 18
• X = 18 or x = -18
               Solve |x| - 2 = 2x + 4
                                  Negate opposite side
•   |x| = 2x + 6                  • |x| = 2x + 6
•   X = 2x + 6                    • X = - (2x + 6)
•   X=-6                          • X = -2x – 6
•   Check in original equation,   • 3x = -6
    not a solution. 4 ≠ -8        • X = -2
                                  • Check in original equation.
                                  • 0=0
                                  • This equation has one
                                    solution.
     Absolute value inequalities
• Solving absolute value inequalities uses the
  same principles as solving absolute value
  equalities. The major issue that must be
  remembered is to change the direction of the
  sign when negating the right side of the
  equation.
                      Solve |x| > 3
First, solve for the positive   Then, multiply right side by -1
• X>3                           • Multiplying by a negative
                                  reverses the sign.

                                • X < -3

                                • The answer is, x < -3 or x > 3
                                • Note the use of the word
                                  “or”.
                      Solve |x| < 3
First solve for the positive   Then multiply by -1
• X<3                          • Remember to reverse the
                                 sign
                               • X > -3
                               • The answer is, x > -3 and x <3
                               • Note the use of the word
                                 “and”.
                               • This may also be written,
                                 -3 < x < 3
             Solve |x| + 8 = 6
• First, combine like terms
• |x| = -2
• No solution
                Remember
• The absolute value symbol must absolutely be
  by itself when solving the equation or
  inequality
• An absolute value is always greater than or
  equal to zero.
• For an inequality, you must reverse the sign
  when multiplying by -1
• Be aware of “and” statements and “or”
  statements.

								
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