The point lies halfway between \(\displaystyle -1\) and \(\displaystyle -2\), or at \(\displaystyle -1.5\).

\(\displaystyle -1.5=-\frac{3}{2}\)

The fraction \(\displaystyle -\frac{7}{3}\) is less than \(\displaystyle -1\) and greater than \(\displaystyle -2\), so it must fall between those points on the number line. Negative numbers are to the left of \(\displaystyle 0\) while positive numbers are to the right.

\(\displaystyle -\frac{7}{3}=-2\frac{1}{3}\)

Because \(\displaystyle \frac{1}{3}\) is less than \(\displaystyle \frac{1}{2}\), the point must be closer to \(\displaystyle -2\) than \(\displaystyle -3\).

To find the distance on a number line:

\(\displaystyle d=x_{2}-x{{_1}}\)

\(\displaystyle d=11-(-4)\)

\(\displaystyle d=11+4\)

\(\displaystyle d=15\)

\(\displaystyle < \) = less than

\(\displaystyle >\) = greater than

\(\displaystyle \leq\) = less than or equal to

\(\displaystyle \geq\) = greater than or equal to

When looking at the number line, we can see that x is any integer between 2 and 7.  

Anything to the right of an integer is considered "greater than" and anything left of an integer is considered "less than".

So, we know that x is greater than 2, but less than 7.

Now, since the circle above the 2 is shaded in, 2 is included in the solution.  The circle above the 7 is not shaded in, so 7 is not included in the solution.

We now know that x is greater than or equal to 2, and it is still less than 7. 

Using the statement above, we will create 2 inequalities.

\(\displaystyle x \geq 2\)

\(\displaystyle x < 7\)

Now, \(\displaystyle x \geq 2\)   can also be written as   \(\displaystyle 2 \leq x\) .  It has the same value, it just looks a little different.

So we have the two inequalities

\(\displaystyle 2 \leq x\)  and \(\displaystyle x < 7\)

We can combine them, and it'll look like this

\(\displaystyle 2 \leq x < 7\)

\(\displaystyle 2.8 = 2.8\)

\(\displaystyle \pi = 3.1415926...\)

\(\displaystyle \sqrt{9} = 3\)

\(\displaystyle \frac{12}{2} = 6\)

\(\displaystyle 10 = 10\)

Thus, in increasing order:

\(\displaystyle 2.8, \sqrt{9}, \pi, \frac{12}{2}, 10\)

When looking at the number line,

we see at -5 there is a filled in circle.  We also see there is an arrow going to the right of -5.  Every integer to the right of -5 is greater than -5 itself.  Because the circle above -5 is filled in, we know -5 is included in the inequality.  We get

\(\displaystyle x \geq -5\)

There is only one negative number in the numbers.

\(\displaystyle -8.43\)

The next biggest is \(\displaystyle 8.2\),

\(\displaystyle -8.43, 8.2\)

Next is \(\displaystyle 8.35\),

\(\displaystyle -8.43, 8.2, 8.35\)

Next is \(\displaystyle 8.5\),

\(\displaystyle -8.43, 8.2, 8.35, 8.5\)

Lastly is \(\displaystyle 8.71\)

\(\displaystyle -8.43, 8.2, 8.35, 8.5, 8.71\)