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Mathematics Dictionary
Subject : Application of prgram ABH on internat
Keyword : Solve abs(x+a) + abs(x+b) = 0

Definition : abs(-1) = |-1| = 1 and abs(1) = 1

Definition : If abs(x-a) = b then (x-a) = b and (x-a) = -b

Subjects

Q1. Solve abs(x-2) = 3

A1. Procedures as below :

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Q2. Sketch graph of y=abs(x-1)+abs(x+1)

A2. Graph is given in ABH program 07 01

* Start software ABH find graphic solution from program 07 01
    1. The slope is +2 and y = +2*x if x > 1
    2. The slope is -2 and y = -2*x if x < -1
    3. The slope is 00 and y = +2 if x between -1 and 1
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Q3. Solve abs(x-2) + abs(x+3) = 6

A3. Grahic solution is given in ABH program 07 03

* Start software ABH find graphic solution from program 07 03
    1. y = +(x-2) + (x+3) if x is greater than 2
    2. y = -(x-2) - (x+3) if x is less than -3
    3. y = 5 if x is between -3 and 2
    3. The solution are the intesections
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Q4. Study graph of y = abs(x+2) + abs(x+3)

A4. Solutions Go to Begin

Q5. Graph of y = abs(x - 1) + abs(x + 1)
  • Graphic is in Program ABH 07 01
  • This equations contains 3 equations :
    • When x GT 1, y = 2*x.
    • When x between -1 and 1, y = 2.
    • When x LT -1, y = -2*x.
Go to Begin

Q06. Solve abs(x - 1) + abs(x + 1) = c
  • Solutions are in Program ABH 07 02
  • Example Solve |x-1| + |x+1| = 3.
    • This equations contains 3 equations :
      • When x GT +1, |x-1| + |x+1| GT 2.
      • When x between -1 and 1, |x-1| + |x+1| = 2.
      • When x LT -1, |x-1| + |x+1| GT 2.
    • Hence there are two roots.
      • When x GT +1, y = 2*x. Hence +2*x = 3 and x = +1.5.
      • When x LT -1, y =-2*x. Hence -2*x = 3 and x = -1.5.
  • Example Solve |x-1| + |x+1| = 1.
    • This equations contains 3 equations :
      • When x GT +1, |x-1| + |x+1| GT 2.
      • When x between -1 and 1, |x-1| + |x+1| = 2.
      • When x LT -1, |x-1| + |x+1| GT 2.
    • Hence there are no solutions.
  • Example Solve |x-1| + |x+1| = 2.
    • This equations contains 3 equations :
      • When x GT +1, |x-1| + |x+1| GT 2.
      • When x between -1 and 1, |x-1| + |x+1| = 2.
      • When x LT -1, |x-1| + |x+1| GT 2.
    • Hence the solution is x between -1 and 1.
Go to Begin

Q10. Instructions and Tips about Program ABH
    * Q1. Read Mathematical Symbols find symbol defintions

    * Q2. How to use the program ABH to find answer from graphs ?
      1. Click start
      2. Click a subject in upper box
      3. Click a program in lower box
      4. Click Back command and repeat step 3 or steps 2 and 3

    * Q3. How to run program 01 03 ?
      1. Start the program ABH
      2. Click Subject 01 in upper box
      3. Click program 03 in lower box

    * Q4. How to start the program ?
      1. Click Program ABH to start
      2. Select run at current location (Donot download)
      3. Select yes to run
Go to Begin

Q11. Reference Go to Begin
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Copyright © Dr. K. G. Shih. Nova Scotia, Canada.
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