# How do you write an inequality and solve given "two thirds of a number added to six is at least twenty two"?

Jul 13, 2017

$x \ge 24$

#### Explanation:

$\text{two-thirds of a number } \rightarrow \frac{2}{3} x$

$\text{added to " 6" } \rightarrow 6 + \frac{2}{3} x$

'Is at least' $22$ means it can be equal to $22$, or more than $22$.

$6 + \frac{2}{3} x \ge 22$

$\frac{2}{3} x \ge 22 - 6$

$\frac{2}{3} x \ge 16$

$\frac{3}{2} \times \frac{2}{3} x \ge \frac{3}{2} \times 16$

$x \ge 24$