Solve (x-7)(x+3)geq0

$$(x-7)(x+3) \geq 0$$

Solve for x

$$x\in (-\infty,-3]\cup [7,\infty)$$

Solution Steps

For the product to be ≥0, x+3 and x-7 have to be both ≤0 or both ≥0. Consider the case when x+3 and x-7 are both ≤0.

$$x+3\leq 0 x-7\leq 0$$

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

$$x\leq -3$$

Consider the case when x+3 and x-7 are both ≥0.

$$x-7\geq 0 x+3\geq 0$$

The solution satisfying both inequalities is x\geq 7.

$$x\geq 7$$

The final solution is the union of the obtained solutions.

$$x\leq -3\text{; }x\geq 7$$