Question

PRECALCULUS HONORS HELP ME PLZ AND THANKS

Answer 1

Inequalities are used to show the relationship between unequal expressions

• The set notation of (5) and (6) are: $\{x : -6 > x \ge -2\}$ and $\{x:-4 < x \ge 6\}$.
• See attachment for the graphs

The following should be notated when plotting the graph of an inequality

• < and > are represented with open circles, while $\leq$ and $\geq$ are represented with closed circles
• The arrows of $<$ and $\le$ point to the left, while the arrows of $>$ and $\geq$ point to the right.

So, we have:

$(a)\ -8 < x$

Rewrite as:

$x > -8$

The graph of $x > -8$ will point to the right, and it will use an open circle

$(b)\ -6 > x \ge -2$

Split the inequality:

$-6 > x$ and $x \ge -2$

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. $-6 > x \ge -2$ cannot be represented on a graph

$(c)\ -4 <x \ge 6$

Split the inequality:

$-4 < x$ and $x \ge 6$

$-4 < x$ means that -4 is less than x or x is greater than -4.

So, we have:

$x > -4$ and $x \ge 6$

If $x > -4$ and $x \ge 6$, then we make use of $x > -4$ because it contains more values of x.

The graph of $x > -4$ will point to the right, and it will use an open circle

Read more about inequalities at:

https://brainly.com/question/11612965