Let's solve the given inequality step-by-step:
Given:
[tex]\[ x - 8 > -3 \][/tex]
1. First, isolate the variable [tex]\( x \)[/tex] by adding 8 to both sides of the inequality:
[tex]\[ x - 8 + 8 > -3 + 8 \][/tex]
[tex]\[ x > 5 \][/tex]
So, the solution to the inequality [tex]\( x - 8 > -3 \)[/tex] is:
[tex]\[ x > 5 \][/tex]
In set notation, the solution set is:
[tex]\[ \{ x \mid x \in \mathbb{R}, x > 5 \} \][/tex]
Now let's choose the correct solution set from the given options:
1. [tex]\(\{ x \mid x \in R, x > -5 \}\)[/tex]
2. [tex]\(\{ x \mid x \in R, x > -9 \}\)[/tex]
3. [tex]\(\{ x \mid x \in R, x > 5 \}\)[/tex]
4. [tex]\(\{ x \mid x \in R, x > 14 \}\)[/tex]
The correct solution set is:
[tex]\[ \{ x \mid x \in \mathbb{R}, x > 5 \} \][/tex]
Thus, the answer is:
[tex]\[ \{ x \mid x \in R, x > 5 \} \][/tex]
