Solving absolute values

Solving absolute values

• 1.
  Copyright © 2011Pearson Education, Inc. Equations Involving Absolute Value 8.28.2 1. Solve equations involving absolute value.
• 2.
  | 3 |= | 0 | = | 2.5 | = | – 7 | = | – 4.8 | = 3 7 4.8 0 2.5 True or False? The absolute value of a number is always positive. False he absolute value of a number ishe absolute value of a number is either positive or 0.either positive or 0. The absolute value of a number isThe absolute value of a number is non-negativenon-negative.. Absolute Value > 0 ≥ 0 Non-negative
• 3.
  | x |= 5 Absolute Value EquationsAbsolute Value Equations x = 5 x = – 5 Same Opposite | x | = –2 No Solution Two Solutions Absolute Value Property If |x| = a, where x is a variable or an expression and a ≥ 0, then x = a or x = −a.
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  SolvingSolving Absolute ValueEquationsAbsolute Value Equations 1. Isolate the absolute value so that the equation is in the form |ax + b| = c. If c < 0, the equation has no solution. 2. Separate the absolute value into two equations, ax + b = c and ax + b = − c. 3. Solve both equations.
• 5.
  Absolute Value EquationsAbsoluteValue Equations 9523 =+− x 423 =− x 55 −− Same Opposite 423 =− xDrop the absolute value bars! Keep the absolute value bars! 423 −=− x 33 −− 12 =− x 22 −− 2 1− =x 33 −− 22 −− 72 −=− x 2 7 =x      − 2 7 2 1 , 1. Isolate 2. Two Cases 3. Solve
• 6.
  Absolute Value EquationsAbsoluteValue Equations 6413 =−−k 1013 =−k 44 ++ Same Opposite 1013 =−kDrop the absolute value bars! Keep the absolute value bars! 1013 −=−k 11 ++ 113 =k 33 3 11 =k 11 ++ 33 93 −=k 3−=k      − 3 11 3, 1. Isolate 2. Two Cases 3. Solve
• 7.
  Absolute Value EquationsAbsoluteValue Equations 7127 =++x 57 −=+x 1212 −− 1. Isolate 2. Two Cases 3. Solve No Solution
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  Absolute Value EquationsAbsoluteValue Equations 052 =+y Same Opposite 052 =+y 55 −− 52 −=y 22 2 5− =y      − 2 5 1. Isolate 2. Two Cases 3. Solve
• 9.
  Opposite Absolute Value Equationswith 2 Absolute ValuesAbsolute Value Equations with 2 Absolute Values | 5 | = | 5 | Same Opposite | –8 | = | –8 | | 5 | = | –5 | | –8 | = | 8 | 4+x ( )4+− x 4−−= x 7−x ( )7−− x 7+−= x 32 +− x ( )32 +−− x 32 −= x Two cases!
• 10.
  Absolute Value Equationswith 2 Absolute ValuesAbsolute Value Equations with 2 Absolute Values 2342 −=+ ww Same Opposite 2342 −=+ ww ( )2342 −−=+ ww      − 6 5 2 , ww 33 −− 24 −=+− w 44 −− 6−=− w 6=w 2342 +−=+ ww 245 =+w ww 33 ++ 44 −− 25 −=w 55 5 2− =w
• 11.
  Absolute Value Equationswith 2 Absolute ValuesAbsolute Value Equations with 2 Absolute Values 332 +=+ kk Same Opposite 332 +=+ kk ( )332 +−=+ kk       −− 2 1 4 5 , kk −− 322 += k 33 −− k21 =− 2 1− =k 332 −−=+ kk 324 −=+k kk 33 ++ 22 −− 54 −=k 44 4 5− =k 22
• 12.
  Absolute Value Equationswith 2 Absolute ValuesAbsolute Value Equations with 2 Absolute Values xx 2392 −=− Same Opposite xx 2392 −=− ( )xx 2392 −−=− { }3 xx 22 ++ 394 =−x 99 ++ 124 =x 3=x xx 2392 +−=− 39 −=− xx 22 −− 44 No Solution