Solve (x+3)(x+2)geq0

$$( x + 3 ) ( x + 2 ) \geq 0$$

Solve for x

$$x\in (-\infty,-3]\cup [-2,\infty)$$

Solution Steps

For the product to be ≥0, x+3 and x+2 have to be both ≤0 or both ≥0. Consider the case when x+3 and x+2 are both ≤0.

$$x+3\leq 0 x+2\leq 0$$

The solution satisfying both inequalities is x\leq -3.

$$x\leq -3$$

Consider the case when x+3 and x+2 are both ≥0.

$$x+2\geq 0 x+3\geq 0$$

The solution satisfying both inequalities is x\geq -2.

$$x\geq -2$$

The final solution is the union of the obtained solutions.

$$x\leq -3\text{; }x\geq -2$$