Solve (x+1)(x+6)geq0

$$( x + 1 ) ( x + 6 ) \geq 0$$

Solve for x

$$x\in (-\infty,-6]\cup [-1,\infty)$$

Solution Steps

For the product to be ≥0, x+6 and x+1 have to be both ≤0 or both ≥0. Consider the case when x+6 and x+1 are both ≤0.

$$x+6\leq 0 x+1\leq 0$$

The solution satisfying both inequalities is x\leq -6.

$$x\leq -6$$

Consider the case when x+6 and x+1 are both ≥0.

$$x+1\geq 0 x+6\geq 0$$

The solution satisfying both inequalities is x\geq -1.

$$x\geq -1$$

The final solution is the union of the obtained solutions.

$$x\leq -6\text{; }x\geq -1$$