Question 48496
| 2/3 x - 2| - 7 > 2
add 7 to both sides
| 2/3 x - 2| > 9
Let 2/3 x = z
| z - 2 | > 9
11 < z < -7
11 < 2/3 x < -7
multiply through by 3
33 < 2x < -21
divide through by 2
33/2 < x < -21/2 answer
check
Let x = 33/2
| 2/3 x - 2| - 7 > 2
|(2/3)(33/2)- 2| - 7 > 2
|11 - 2| - 7 > 2
9 - 7 > 2
2 > 2
false, so x > 33/2
Let x = -21/2
| 2/3 x - 2| - 7 > 2
| (2/3)(-21/2) - 2| - 7 > 2
| -7 -2| -7 > 2
9 - 7 > 2
2 > 2
false, so x < -21/2