# How do you solve and write the following in interval notation: (2x + 3)(x − 1) ≥ 0?

Jul 11, 2016

$x \notin \left(- \frac{3}{2} , 1\right)$

#### Explanation:

Both (2x+3) and (x-1) should be either $\ge 0$ or $\le 0$

For $2 x + 3 \ge 0 \mathmr{and} x - 1 \ge 0 , x \ge - \frac{3}{2} \mathmr{and} x \ge 1$..

Here, $x \ge 1$ includes $x \ge - \frac{3}{2}$.

Likewise, for the other case, $x \le - \frac{3}{2}$.

Combining both, $x \notin \left(- \frac{3}{2} , 1\right)$..