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What is the solution to the inequality [tex]\( 28 \ \textgreater \ 4 - 2p \)[/tex] ?

A. [tex]\( \{ p \mid p \ \textgreater \ -12 \} \)[/tex]
B. [tex]\( \{ p \mid p \ \textless \ -12 \} \)[/tex]
C. [tex]\( \{ p \mid p \ \textgreater \ 12 \} \)[/tex]
D. [tex]\( \{ p \mid p \ \textless \ 12 \} \)[/tex]

Sagot :

GinnyAnswer
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]
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