Solve (x+2)(5-x)leq0

$$(x+2)(5-x) \leq 0$$

Solve for x

$$x\in (-\infty,-2]\cup [5,\infty)$$

Solution Steps

For the product to be ≤0, one of the values x+2 and 5-x has to be ≥0 and the other has to be ≤0. Consider the case when x+2\geq 0 and 5-x\leq 0.

$$x+2\geq 0 5-x\leq 0$$

The solution satisfying both inequalities is x\geq 5.

$$x\geq 5$$

Consider the case when x+2\leq 0 and 5-x\geq 0.

$$5-x\geq 0 x+2\leq 0$$

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

$$x\leq -2$$

The final solution is the union of the obtained solutions.

$$x\geq 5\text{; }x\leq -2$$