To solve the inequality [tex]\(28 > 4 - 2p\)[/tex], follow these steps:
1. Isolate the term with [tex]\(p\)[/tex] on one side of the inequality:
[tex]\[
28 > 4 - 2p
\][/tex]
Subtract 4 from both sides to isolate the term involving [tex]\(p\)[/tex]:
[tex]\[
28 - 4 > -2p
\][/tex]
Simplifying the left side:
[tex]\[
24 > -2p
\][/tex]
2. Isolate [tex]\(p\)[/tex] by eliminating the coefficient [tex]\(-2\)[/tex]:
To isolate [tex]\(p\)[/tex], divide both sides of the inequality by [tex]\(-2\)[/tex]. When dividing both sides of an inequality by a negative number, the direction of the inequality sign must be reversed:
[tex]\[
\frac{24}{-2} < p
\][/tex]
Simplifying:
[tex]\[
-12 < p
\][/tex]
Which can be written as:
[tex]\[
p > -12
\][/tex]
So, the solution to the inequality is [tex]\(\{p \mid p > -12\}\)[/tex]. Therefore, the correct option is:
[tex]\[
\boxed{\{p \mid p > -12\}}
\][/tex]
