# List all of the the restricted values sqrt 2x - 5?

##### 1 Answer
Apr 2, 2017

Assumption: the question is: $\sqrt{2 x - 5}$

$x < \frac{5}{2}$

Written in set notation as $\left\{x : x \in \left(- \infty , \frac{5}{2}\right)\right\}$

In this context the rounded brackets mean 'not including'. I have seen it written as: $\left\{x : x \in \textcolor{w h i t e}{\frac{.}{.}}\right] \textcolor{w h i t e}{.} - \infty , \frac{5}{2} \left[\textcolor{w h i t e}{\frac{.}{.}}\right\}$

#### Explanation:

To force the mathematical formatting you use the hash symbol at the beginning and end of the 'maths bit'.

I wrote the form$\text{ }$ hash sqrt(2x - 5) hash$\text{ }$ to get $\sqrt{2 x - 5}$

For the numbers to stay a belong to the set of 'Real numbers' you need to make sure that $2 x - 5 \ge 0$

$2 x - 5 \ge 0$

add 5 to both sides

$2 x \ge 5$

divide both sides by 2

$x \ge \frac{5}{2}$

So the restricted value are all those that do not comply with $x \ge \frac{5}{2}$ and these are $x < \frac{5}{2}$