Question

For the following inequality, write the solution set in set-builder and interval notation, and graph the solution seton a number line.X_>2Set-builder notation: {x| }Interval notation:

Answer 1

Answer: $\begin{gathered} a)\text{ }\lbrace x\text{ \mid x }\ge\text{ 2\textbraceright} \\ b)\text{ \lbrack2, }\infty) \end{gathered}$

See graph below

Explanation:

Given:

$x\text{ \ge 2}$

To find:

to write in set builder notation, interval notation and graph the inequality

a) In set-builder notation:

$\begin{gathered} \lbrace x\in\Re\text{ \mid x }\ge\text{ 2\textbraceright} \\ \lbrace x\text{\mid x }\ge\text{ 2\textbraceright} \end{gathered}$

b) Interval notation:

$\begin{gathered} [\text{ \rbrack represents inequality with an equal sign or that the number is inclusive} \\ (\text{ })\text{ shows that the number is not inclusive} \\ Notation:\text{ \lbrack2, }\infty) \end{gathered}$

c) Graphing the inequality on a number line:

The circle is shaded because the inequality has an equal sign attached