To solve the inequality [tex]\(5 - (x + 5) > -2(x + 4)\)[/tex], let's follow these steps:
1. Distribute the terms inside the parentheses:
[tex]\[
5 - x - 5 > -2x - 8
\][/tex]
2. Combine like terms on the left side of the inequality:
[tex]\[
5 - 5 - x > -2x - 8
\][/tex]
Simplifying this, we get:
[tex]\[
-x > -2x - 8
\][/tex]
3. Isolate the variable [tex]\(x\)[/tex] on one side of the inequality. To do this, add [tex]\(2x\)[/tex] to both sides:
[tex]\[
-x + 2x > -2x + 2x - 8
\][/tex]
Simplifying this, we obtain:
[tex]\[
x > -8
\][/tex]
Thus, the solution to the inequality [tex]\(5 - (x + 5) > -2(x + 4)\)[/tex] is:
[tex]\[
x > -8
\][/tex]
