Inequalities are used to show the relationship between unequal expressions
- The set notation of (5) and (6) are: [tex]\{x : -6 > x \ge -2\}[/tex] and [tex]\{x:-4 < x \ge 6\}[/tex].
- See attachment for the graphs
The following should be notated when plotting the graph of an inequality
- < and > are represented with open circles, while [tex]\leq[/tex] and [tex]\geq[/tex] are represented with closed circles
- The arrows of [tex]<[/tex] and [tex]\le[/tex] point to the left, while the arrows of [tex]>[/tex] and [tex]\geq[/tex] point to the right.
So, we have:
[tex](a)\ -8 < x[/tex]
Rewrite as:
[tex]x > -8[/tex]
The graph of [tex]x > -8[/tex] will point to the right, and it will use an open circle
[tex](b)\ -6 > x \ge -2[/tex]
Split the inequality:
[tex]-6 > x[/tex] and [tex]x \ge -2[/tex]
It is not possible for -6 to be less than x and at the same time, x is greater than or equal to -2.
Hence. [tex]-6 > x \ge -2[/tex] cannot be represented on a graph
[tex](c)\ -4 <x \ge 6[/tex]
Split the inequality:
[tex]-4 < x[/tex] and [tex]x \ge 6[/tex]
[tex]-4 < x[/tex] means that -4 is less than x or x is greater than -4.
So, we have:
[tex]x > -4[/tex] and [tex]x \ge 6[/tex]
If [tex]x > -4[/tex] and [tex]x \ge 6[/tex], then we make use of [tex]x > -4[/tex] because it contains more values of x.
The graph of [tex]x > -4[/tex] will point to the right, and it will use an open circle
Read more about inequalities at:
https://brainly.com/question/11612965
