Let's solve the given inequality step-by-step:
Given inequality:
[tex]\[ x - 5 > -2 \][/tex]
To isolate [tex]\( x \)[/tex], we will add 5 to both sides of the inequality. This step ensures that [tex]\( x \)[/tex] is by itself on the left side.
[tex]\[ x - 5 + 5 > -2 + 5 \][/tex]
Simplifying both sides, we get:
[tex]\[ x > 3 \][/tex]
Thus, the solution set for this inequality is the set of all [tex]\( x \)[/tex] such that [tex]\( x \)[/tex] is greater than 3.
Now, let's match this with the given choices:
1. [tex]\([x \mid x \in R, x > -7]\)[/tex]
2. [tex]\(\{x \mid x \in R, x > -3\}\)[/tex]
3. [tex]\(\{x \mid x \in R, x > 3\}\)[/tex]
4. [tex]\([x \mid x \in R, x > 7]\)[/tex]
The correct solution set is:
[tex]\(\{x \mid x \in R, x > 3\}\)[/tex]
So, the solution set for the given inequality [tex]\( x - 5 > -2 \)[/tex] is [tex]\(\{x \mid x \in R, x > 3\}\)[/tex].
