To find the solution set of the inequality [tex]\( x + 2 > -4 \)[/tex], let's solve it step-by-step:
1. Identify the inequality:
The given inequality is:
[tex]\[
x + 2 > -4
\][/tex]
2. Isolate [tex]\( x \)[/tex] on one side of the inequality:
To isolate [tex]\( x \)[/tex], we need to get rid of the constant term (which is 2) on the left side. We do this by subtracting 2 from both sides of the inequality:
[tex]\[
x + 2 - 2 > -4 - 2
\][/tex]
3. Simplify both sides:
Simplifying both sides, we get:
[tex]\[
x > -6
\][/tex]
Therefore, the solution set for the inequality [tex]\( x + 2 > -4 \)[/tex] is:
[tex]\[
\{x: x > -6\}
\][/tex]
The correct answer from the given choices is:
G. [tex]\(\{x: x > -6\}\)[/tex]
