Question

Tentukan nilai x yang memenuhi persamaan
Tentukan himpunan penyelesaiannya!
1.) |x| + |x+2| = 4
2.) |x-1| + |x+3| = 5
3.) |2x-1| + |3x-2| = 3
4.) |x+2| + |2x-3| = 4
5.) |x-2| + |5-2x| = 2
6.) |x+1| + |2x| + |3x-5| =7

Answer 1

1) | x| + | x+2| = 4
x> 0 , x+2 > 0
x + x + 2 = 4
2x = 2
x = 1

x < 0 , x +2 < 0
-x - x - 2 = 4
-2x = 6
x = -3

2) |x-1| + |x +3| = 5
x -1 + x + 3 = 5
2x = 3
x = 3/2

x-1 <0 , x+3 < 0
-x + 1 - x - 3 = 5
-2x - 2 = 5
x = - 72

3) |2x -1| + |3x -2| = 3
2x -1 > 0 , 3x -2 > 0
2x -1 + 3x - 2 = 3
5x -3 = 3
x = 6/5

2x-1 < 0 , 3x -2 < 0
1-2x  + 2 - 3x = 3
-5x+3= 3
x = 0

4) |x+2| + |2x-3| = 4
x + 2 + 2x - 3 = 4
3x - 1= 4
x= 5/3

-x - 2 - 2x + 3 = 4
-3x + 1 = 4
x = 1

5) |x -2| + |5 - 2x| = 2
x - 2 + 2x - 5 = 2
3x - 7 = 2
x = 3

2 - x + 5 - 2x = 2
-3x + 7 = 2
x = 5/3

6) |x+1| +|2x| + |3x -5| = 7
|x+1| + 2|x| + |3x -5| = 7
x+1 + 2x+ 3x - 5 = 7
6x - 4 = 7
x = 11/6

x + 1 - 2x -3x + 5 = 7
-4x + 6 = 7
x = -1/4