Solving (x-3)(x+1)+(x-3)(x+2)≥0 with interval table

[eleventhxhour]

Solve the following inequality:

6e) $(x - 3)(x + 1) + (x - 3)(x + 2) \ge 0$

So, I created an interval table with the zeros x-3, x+1, x-3 and x+2 but I keep getting the wrong answer. Could someone help? (this is grade 12 math - so please don't be too complicated).

Thanks.

 

[Siron]

I would start with factoring the LHS:
$$(x-3)[(x+1)+(x+2)] \geq 0$$
$$\Leftrightarrow (x-3)(2x+3) \geq 0$$

Now create an interval table and look where the function $f(x)=(x-3)(2x+3)$ which has two zeros at $x=3$ and $x=\frac{-3}{2}$ is positive. That will give you the answer.