1.7 Solving Absolute Value Equations

1.7 Solving Absolute Value Equations

• 1.
  1.7 Solving AbsoluteValue Equations
• 2.
  Solving an AbsoluteValue Equation • Absolute value equations can have two solutions. • For example, |x| = 5 could have solutions x = 5 or x = -5 • To solve |ax + b| = c, write as two equations: ax + b = c or ax + b = -c, then solve both.
• 3.
  Example: • Solve |2x– 5| = 9
• 4.
  Example: • Solve |x– 3| = -4
• 5.
  Your Turn! • Solve|6x – 3| = 15
• 6.
  Solving Inequalities: |ax+ b|  c • |ax + b|  c means ax + b is between –c and c • Rewrite as an “and” compound inequality, then solve. -c < ax + b < c
• 7.
  Example: • Solve |2x+ 7| < 11 and graph the solution on a number line.
• 8.
  Your Turn! • Solve|-x + 5|  6 and graph the solution.
• 9.
  Solving Inequalities: |ax+ b| > c • |ax + b| > c means ax + b is beyond –c and c • Rewrite as an “or” compound inequality, then solve. ax + b < -c or ax + b > c
• 10.
  Example: • Solve |3x– 2|  8 and graph the solution.
• 11.
  Your Turn! • Solve|x + 5| > 12 and graph the solution.