91Ó°ÊÓ

The given equations are

$\begin{array}{l}a)x<−2\\ b)xâ‰\yen −3.5\\ c)x≤\frac{2}{3}\end{array}$

We have to plot each inequality on the number line and then write in interval notation.

Consider the equation $x≤−2$.

Now,

x ≤ -2 means all numbers less than or equal to -2.

Therefore, we shade in all the numbers on the number line to the left of -2 and put a solid circle at x = -2 to show that it is included.

The graph will be as shown below.

Now,

x ≤ -2 means all numbers less than or equal to -2.

Therefore, put a square bracket x = -2 to show that it is included and an open bracket for negative infinity.

Thus,

The notation will be$[-2,-∞).$

Consider the equation $xâ‰\yen −3.5$.

Now,

$xâ‰\yen −3.5$means all numbers greater than or equal to $−3.5$.

Therefore, we shade in all the numbers on the number line to the right of $−3.5$and put a solid circle at $−3.5$to show that it is included.

The graph will be as shown below.

Now,

$xâ‰\yen −3.5$means all numbers less than or equal to $−3.5$.

Therefore, put a square bracket $xâ‰\yen −3.5$to show that it is included and an open bracket for infinity.

Thus,

The notation will be$[−3.5,∞)$.

Consider the equation$x≤\frac{2}{3}$.

Now,

$x≤\frac{2}{3}$means all numbers less than or equal to$\frac{2}{3}$.

Therefore, we shade in all the numbers on the number line to the left of $\frac{2}{3}$and put a solid circle at $x=\frac{2}{3}$to show that it is included.

The graph will be as shown below.

Now,

$x≤\frac{2}{3}$means all numbers less than or equal to $\frac{2}{3}$.

Therefore, put a square bracket before $\frac{2}{3}$ to show that it is included and an open bracket for negative infinity.

Thus,

The notation will be$[\frac{2}{3},−∞)$