Solve (2x-136)(x+82)geq0

$$( 2 x - 136 ) ( x + 82 ) \geq 0$$

Solve for x

$$x\in (-\infty,-82]\cup [68,\infty)$$

Solution Steps

For the product to be ≥0, x+82 and 2x-136 have to be both ≤0 or both ≥0. Consider the case when x+82 and 2x-136 are both ≤0.

$$x+82\leq 0 2x-136\leq 0$$

The solution satisfying both inequalities is x\leq -82.

$$x\leq -82$$

Consider the case when x+82 and 2x-136 are both ≥0.

$$2x-136\geq 0 x+82\geq 0$$

The solution satisfying both inequalities is x\geq 68.

$$x\geq 68$$

The final solution is the union of the obtained solutions.

$$x\leq -82\text{; }x\geq 68$$