91Ó°ÊÓ

The given equations are

$\begin{array}{l}a)x>3\\ b)x≤−0.5\\ c)xâ‰\yen \frac{1}{3}\end{array}$

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

Consider the equation $x>3$.

Now,

$x>3$means all numbers greater than 3.

Therefore, we shade in all the numbers on the number line to the right of 3 and put a hollow circle at x = 3 to show that it is not included.

The graph will be as shown below.

Now,

x < 3 means all numbers greater than 3.

Therefore, put an open bracket to show that 3 and infinity are not included.

Thus,

The notation will be$(3,∞).$

Consider the equation $x≤−0.5$.

Now,

$x≤−0.5$means all numbers less than and equal to -0.5.

Therefore, we shade in all the numbers on the number line to the left of -0.5 and put a solid circle at x = -0.5 to show that it is included.

The graph will be as shown below.

Now,

$x≤−0.5$means all numbers less than or equal to $x≤−0.5$.

Therefore, put a square bracket before $−0.5$to show that it is included and an open bracket for negative infinity.

Thus,

The notation will be $[−0.5,−∞)$.

Consider the equation $xâ‰\yen \frac{1}{3}$.

Now,

$xâ‰\yen \frac{1}{3}$means all numbers greater than and equal to$\frac{1}{3}$.

Therefore, we shade in all the numbers on the number line to the right of $\frac{1}{3}$and put a solid circle at $x=\frac{1}{3}$ to show that it is included.

The graph will be as shown below.

Now,

$xâ‰\yen \frac{1}{3}$means all numbers greater than or equal to $\frac{1}{3}$.

Therefore, put a square bracket before$\frac{1}{3}$ to show that it is included and an open bracket for infinity.

Thus,

The notation will be$[\frac{1}{3},∞)$.