Solve left(2x+1right)left(x-2right)geq0

$$\left( 2x+1 \right) \left( x-2 \right) \geq 0$$

Solve for x

$$x\in (-\infty,-\frac{1}{2}]\cup [2,\infty)$$

Solution Steps

For the product to be ≥0, 2x+1 and x-2 have to be both ≤0 or both ≥0. Consider the case when 2x+1 and x-2 are both ≤0.

$$2x+1\leq 0 x-2\leq 0$$

The solution satisfying both inequalities is x\leq -\frac{1}{2}.

$$x\leq -\frac{1}{2}$$

Consider the case when 2x+1 and x-2 are both ≥0.

$$x-2\geq 0 2x+1\geq 0$$

The solution satisfying both inequalities is x\geq 2.

$$x\geq 2$$

The final solution is the union of the obtained solutions.

$$x\leq -\frac{1}{2}\text{; }x\geq 2$$