1) To solve -3x > -9, we need to divide by -3 on both sides to isolate x. Remember that when dividing or multiplying by a negative number, the inequality sign flips.

So, we have:

x < 3

Therefore, the solution to the inequality -3x > -9 is x < 3.

2) Let's simplify the given inequality step by step:

2(x-3) - 1 > 3(x-2) - 4(x+1)

Distribute on both sides:

2x - 6 - 1 > 3x - 6 - 4x - 4

Combine like terms:

2x - 7 > -x - 10

Add x to both sides:

3x - 7 > -10

Add 7 to both sides:

3x > -3

Divide by 3 on both sides:

x > -1

Therefore, the solution to the inequality 2(x-3) - 1 > 3(x-2) - 4(x+1) is x > -1.

3) To solve (x-0.5)(x-2)(x+3) > 0, we need to find the intervals where the expression is greater than zero. We can do this by considering the sign of each factor separately.

1) (x - 0.5):

This factor is positive when x > 0.5

2) (x - 2):

This factor is positive when x > 2

3) (x + 3):

This factor is positive when x > -3

Now, we need to find the overlap of these intervals to get the final solution.

The expression is positive when:

x > 2 (from the factor x - 2)x > 0.5 (from the factor x - 0.5)x > -3 (from the factor x + 3)

Therefore, the solution to the inequality (x-0.5)(x-2)(x+3) > 0 is x > 2.