To solve the inequality [tex]\(2a + 4 > 12\)[/tex], follow these steps:
1. Subtract 4 from both sides:
[tex]\[
2a + 4 - 4 > 12 - 4
\][/tex]
Simplifying this, we get:
[tex]\[
2a > 8
\][/tex]
2. Divide both sides by 2:
[tex]\[
\frac{2a}{2} > \frac{8}{2}
\][/tex]
Simplifying this, we get:
[tex]\[
a > 4
\][/tex]
Hence, the solution to the inequality [tex]\(2a + 4 > 12\)[/tex] is [tex]\(\{a \mid a > 4\}\)[/tex].
Among the given options, the correct solution is:
[tex]\[
\{a \mid a > 4\}
\][/tex]
