Question

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

Answer 1

We have a inequality defined as:

$x\leq\frac{2}{3}$

We have to express it in set-builder notation.

We can do it directly as:

$\lbrace x|x\leq2\/3\rbrace$

If we have to express it in interval notation we can express all the values of x that are equal to or less than 2/3 as:

$x\in(-\infty,2\/3]$

Finally we can graph this in a number line as:

Answer:

Set-builder notation: { x | x ≤ 2/3 }

Interval notation: (-∞, 2/3]

Number line: picture in the answer