1) 2x - 3(x+1) > 2 + x2x - 3x - 3 > 2 + x-x - 3 > 2 + x-x - x > 2 + 3-2x > 5x < -5/2
2) -x^2 + 3x - 2 < 0-x^2 + 3x < 2x(3 - x) < 22 < x < 3
3) (x+6)(x+2) < 0The solutions for this inequality are x < -6 and -2 < x < 0
4) x^2 < 49Taking the square root of both sides, we get:x < 7 and x > -7
5) x^2(3x-2)(x-8) < 0The solution for this inequality is -8 < x < 0 and 2/3 < x < 8-8 < x < 02/3 < x < 8
1) 2x - 3(x+1) > 2 + x
2x - 3x - 3 > 2 + x
-x - 3 > 2 + x
-x - x > 2 + 3
-2x > 5
x < -5/2
2) -x^2 + 3x - 2 < 0
-x^2 + 3x < 2
x(3 - x) < 2
2 < x < 3
3) (x+6)(x+2) < 0
The solutions for this inequality are x < -6 and -2 < x < 0
4) x^2 < 49
Taking the square root of both sides, we get:
x < 7 and x > -7
5) x^2(3x-2)(x-8) < 0
The solution for this inequality is -8 < x < 0 and 2/3 < x < 8
-8 < x < 0
2/3 < x < 8