Question

1)
| a + 1 | = 2a -3
2)

3)
|-2x| + 5 = 13
4)
|5x + 10 | = -|3x +6|
5)

Answer 1

Verified answer

Jawab

1)
|a + 1| = 2a - 3

(i)
a + 1 = 2a - 3
a - 2a = - 3 - 1
- a = - 4
a = 4

(ii)
-a -1 = 2a - 3
-a - 2a =- 3 + 1
-3a = - 2
a= 2/3 (tidak memenuhi), sebab jika di sub ke soal |a+1| = 2a - 3
|2/3 + 1| = 2(2/3)  - 3
| 5/3 | = 4/3 - 3
|5/3| = - 5/3 --> nilai mutlak tidak negatif

hp a = 4

2)
|4 -  2/5 x| - 7 = 13
|4 - 2/5 x | = 13 + 7
|4 - 2/5 x| = 20

(i)
4 - 2/5 x = 20 
20 - 2x = 100
-2x =  80
x = - 40

2/5x - 4 = 20
2/5x = 24
x = 60
HP (-40, 60)

3.
|2x|  + 5 = 13
|2x| = 8
2x= 8 atau -2x = 8
x = 4  atau x = - 4

4.
|5x +10| =  -|3x - 6|
tidak ada penyelesaian ,krn nilai mutlak positif

5.
2 < | 2 - x/2| ≤ 3

(i) 
| 2 - x/2| ≤3

-3 ≤ 2 - x/2 ≤ 3
-3 - 2 ≤ - x/2 ≤ 3 + 2
- 5 ≤ -x/2 ≤ 5
-10  ≤ -x ≤ 5
x ≥-  5  atau x ≤ 10

(ii) 
|2 - x/2 | > 2
- 2 > 2 - x/2 > 2
- 4  > - x/2 > 4
- 8 > - x > 8

-x > 8 -->x < -8
-x < - 8 --> x > 8

(I) dan (ii) 
x ≥ -5, x ≤10
x< -8 , x > 8 

HP x < - 8 tau 8 <x ≤10