Let's solve the given inequality step by step.
We start with the inequality:
[tex]\[ x - 5 > -2 \][/tex]
To isolate [tex]\( x \)[/tex], we need to remove the constant term on the left side of the inequality. We do this by adding 5 to both sides of the inequality.
[tex]\[ x - 5 + 5 > -2 + 5 \][/tex]
Simplify both sides:
[tex]\[ x > 3 \][/tex]
The solution set of the inequality [tex]\( x > 3 \)[/tex] in set-builder notation is:
[tex]\[ \{x \mid x \in \mathbb{R}, x > 3\} \][/tex]
Among the given options, the correct solution set is:
[tex]\[ \{x \mid x \in R, x > 3\} \][/tex]
Therefore, the correct choice is:
[tex]\[ \{x \mid x \in R, x > 3\} \][/tex]
