Question

1) | x +4 | <6
2 | 3x -1 | >8
3) | x+3| < | 2x -3|

Answer 1

Verified answer

No. 1
| x +4 | <6
-6 < x + 4 < 6
-6 - 4 < x < 6 - 4
-10 < x < 2

HP : {x| -10 < x < 2}

No. 2
| 3x -1 | >8
(i)
3x - 1 > 8
3x -1 + 1 > 8 + 1
3x > 9
x > 3
(ii)
3x - 1 < -8
3x - 1 + 1 < -8 + 1
3x < -7
x < -7/3
HP : {x| x < -7/3  atau  x > 3}

No. 3
|x + 3| < | 2x - 3 |
(x + 3)² < (2x - 3)²
x² + 6x + 9 < 4x² - 12x + 9
4x² - 12x > x² + 6x
3x² - 18x > 0
3x(x - 6) > 0

+ + + + +    - - - - - - - -    + + + + +
_______0__________6_______
jadi HP : {x| x < 0  atau x > 6}