Soal persamaan dan pertidaksamaan nilai mutlak linear satu variabel

1. Hasil hari |12|- |-3| =...
    Jawab :
   |12|- |-3|
  = 12 - 3
  =  9

2.  |-24/36| x |-6|=...
    Jawab :
     |-24/36| x |-6|
    = 24/36 x 6
    = 24/6
    = 4

3. Hasil dari |2 x 4 - 10| - |1-2 x 3| x |1 +2|
     Jawab :
    | 2 x 4 - 10| - |1- 2 x 3| x |1 + 2 |
  = | 8 - 10| - | 1-6 | x | 3 |
  = | -2 | - |-5 | x | 3|
  =    2  - 5 x 3
  =   2 -15
  =  - 13

4. | 5 | - 3 x |4/-3| + |-2 |^2
     Jawab :
=  5 - 3 x 4/3 + 4
=  5 - 4 + 4
=  1 + 4
=  5

5.Hasil dari | - a | x | a | - | -a^2| x (-2)=...
     Jawab :
=  a x a - a ^2 x -2
=  a ^2 +2 a^2
= 3 a^2

6.Nilai |10 + x - x ^2| untuk x = 20 adalah..
     Jawab :
  = |10 + (20) - (20)^2 |
  = | 10 + (20) - 400|
  = | 30 - 400|
  = | - 370|
  = 370
 
7.Diketahui f(x) = |x - 5|
   Nilai f(0) + f(5) - f(10) x f(-2 ) =...
      Jawab :
   f (0) = | 0 - 5 |       
           = | -5 |
           = 5
   f (5 ) = |5- 5|
             = | 0 |
             =  0
    f (10) = | 10 - 5 |
               = | 5 |
               =  5
   f ( -2) = | -2 - 5|
              = | - 7 |
              =  7

* f(0)+ f (5) - f (10) x f(-2)
= 5 +0 - 5 x 7
= 5+0-35
= 5 - 35
= -30

8 Diketahui f(x) = |2 x - 1| dan g(x ) = |5 - x|.Nilai f( 3) - g (3)=...
    Jawab :
  f(x) = | 2x - 1|
  f(3) = | 2 x 3 - 1|
          = | 6 - 1|
          = | -5 |
          = 5
g (x)  = | 5 - x |
  g (3) = | 5 - 3|
            = | 2 |
            = 2
  * f (3) - 9(3)
   = 5 - 2
   = 3

9 Bentuk sederhana dari |x + 4| + |5- 2x| - |x -2| untuk nilai x >10 adalah
Note »maaf karena keyboardnya gak ada lambangnya lebih dari/sama dgn satu
>_: lebih dari atau sama dengan satu
< : kurang dari
    Jawab :
(+) x + 4 >_0
              x >_ -4.    √
( - ) x + 4 < 0
                x < - 4.      X

(+) 5- 2x >_ 0
          -2x >_ -5
             x <_ -5/-2.    X
             x <_ 5/2
(- ) 5 - 2x <0
            - 2x <-5
                x >-5/-2
                 x >5/2.      √

(+ ) x - 2 >_0
              x >_2      √
  ( - ) x - 2 < 0
              x <2      X

* | x + 4 | + | 5 - 2 x | - | x - 2|
= (x + 4) + - ( 5 - 2x)  - ( x - 2)
= x + 4 -5 + 2x - x + 2
= x + 2x - x + 4 - 5 + 2
= 3x - x +1
= 2x + 1

10. Bentuk sederhana dari |3x - 6|- |x - 4| |x + 1| untuk nilai 2 < x < 4 adalah...
     Jawab :
(+)3 x - 6 >_0
             3x >_6
               x >_6/3     √
               x >_ 2
(-) 3x - 6 < 0
            3 x <6
               x < 6 /3       X
               x < 2

(+) x - 4 >_ 0
           x >_4            X
(-)  x - 4 < 0
            x < 4               √

(+) x + 1 >_0
            x >_ -1            √
(-) x + 1 < 0
           x < -1            X

* | 3 x - 6 | - | x - 4 | |x +1|
= (3x - 6 ) - (-(x - 4 ) ( x + 1)
= 3 x - 6 +( x - 4 ) (x +1 )
= 3x - 6 + x^2 + x - 4 x -4
= x^2 + 3x - 4 x + x - 6 -4
= x^2 - 10
    
B. Kerajakan soal - soal berikut
1a.|2|| - 12|-|6||-3^2|
   Jawab:
   = 2 . 12 - 6. 9
   = 24 - 54
   = - 30
  b. |5/-2 x 3| |-24| (- |1/6|)
    Jawab :
   = |15/-2| |-24| ( - 1/6)
   =  15/2 . 24 . -1/6
   =  15.12.-1/6
   =  15.2.-1
   =   -30

2.Gambarlah fungsi mutlak berikut.
  a. f(x) = |3x - 2|
      * f (-4) = | 3.-4 -2|
                  = |- 12 - 2|
                  = | - 14|
                  =  14
      * f(-3)  = | 3.-3 - 2 |
                  =  | -9 -2 |
                  =  | - 11|
                  =   11
     * f(-2)  = |3.-2 -2|
                  = | -6 -2|
                  = |-8|
                  =  8
     * f(-1)  = |3.-1-2|
                 = |-3 -2 |
                 = | -5|
                 = 5
     * f (0)  = |3.0-2|
                 = |0-2|
                 = |-2|
                 = 2
     *  f (1) = |3.1- 2|
                 = |3 - 2|
                 = | 1|
                 = 1
      * f (2) = |3.2 -2 |
                 = | 6 -2| 
                 = | 4 |
                 =  4
      * f(3) = |3.3-2|  
                = |9 -2|
                = |7|
                = 7
      * f(4) = |3.4 - 2|
                = | 12 -2 |
                = |10|
                = 10

Note : Maaf teman - teman, dasbor blogernya lagi rewel gak bisa masukin gambar grafiknya

b. g(x) = |x+4| - 6
* g (-4) = |-4+4| -6
              = |0| -6
              = -6
* g(-3) = |-3 + 4|-6
            = | 1| - 6
            =  1- 6
            = -5
* g(-2) = |-2+4|-6
            = |2| -6
            = 2-6
            = -4
* g(-1)= |-1+ 4| -6
           = |3 | -6
           = 3-6
           = -3
* g(0) = |0+4| -6
           = |4| -6
           = 4 - 6
           = -2
* g(1) = |1+4| -6
           = |5| -6
           = 5-6
           = -1
* g(2)= |2+4| -6
          = |6| -6
          = 6-6
          = 0
*g(3) = |3+4|-6
          = |7| -6
          = 7-6
          = 1
*g(4) = |4 +4|-6
          = |8|-6
          = 8-6
          = 2
Note : Maaf teman - teman, dasbor blogernya lagi rewel gak bisa masukin gambar grafiknya

3.Diketahui f (x) = |3x+9|
   Tentukan nilai (f(-4) x f(-1) + f(3)/|-3|)
    Jawab :
  f(-4) = |3.-4 + 9|
           = | -12 + 9|
           = |-3|
           = 3
  f(-1) = |3.-1 + 9|  
           = |-3 +9|
           = |6|
           = 6
  f(3)  = |3.3+ 9|
           = |9 + 9|
           = | 18|
           = 18
* (f(-4)x f(-1)+f(3)/|-3|)
= 3 x 6+18/3
= 18 + 18/3
= 18 + 6
= 24

      
 
   

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