Solve (x+4)(x-1)geq0

$$(x+4)(x-1) \geq 0$$

Solve for x

$$x\in (-\infty,-4]\cup [1,\infty)$$

Solution Steps

For the product to be ≥0, x+4 and x-1 have to be both ≤0 or both ≥0. Consider the case when x+4 and x-1 are both ≤0.

$$x+4\leq 0 x-1\leq 0$$

The solution satisfying both inequalities is x\leq -4.

$$x\leq -4$$

Consider the case when x+4 and x-1 are both ≥0.

$$x-1\geq 0 x+4\geq 0$$

The solution satisfying both inequalities is x\geq 1.

$$x\geq 1$$

The final solution is the union of the obtained solutions.

$$x\leq -4\text{; }x\geq 1$$