# How do you solve and write the following in interval notation: (2/3)x – (4/3) ≥ (1/4)?

Aug 19, 2016

$x \ge \frac{9}{4} \to \left[\frac{9}{4} , \infty\right)$

[ means inclusive or closed; whilst ) means exclusive or open
So the interval includes $\frac{9}{4}$ but excludes $\infty$

#### Explanation:

Lets get rid of the fractions!

Change the denominators to 12

$\left(\frac{2}{3} \times \frac{4}{4}\right) x - \left(\frac{4}{3} \times \frac{4}{4}\right) \ge \left(\frac{1}{4} \times \frac{3}{3}\right)$

$\frac{8}{12} x - \frac{16}{12} \ge \frac{3}{12}$

It is also true that

$8 x - 16 \ge 3$

$8 x \ge 18$

divide both sides by 8

$x \ge \frac{18}{8} \equiv \frac{9}{4}$