To solve the inequality [tex]\(-2x - 8 > 5x + 13\)[/tex], follow these steps:
1. Isolate the variable on one side:
Start by moving all terms involving [tex]\(x\)[/tex] to one side of the inequality and constants to the other side. Subtract [tex]\(5x\)[/tex] from both sides:
[tex]\[
-2x - 8 - 5x > 5x + 13 - 5x
\][/tex]
2. Combine like terms:
Simplify the inequality by combining the [tex]\(x\)[/tex] terms on the left side and the constants on the right side:
[tex]\[
-7x - 8 > 13
\][/tex]
3. Isolate the [tex]\(x\)[/tex] term:
Add [tex]\(8\)[/tex] to both sides of the inequality to move the constants to one side:
[tex]\[
-7x - 8 + 8 > 13 + 8
\][/tex]
[tex]\[
-7x > 21
\][/tex]
4. Solve for [tex]\(x\)[/tex]:
Finally, divide both sides by [tex]\(-7\)[/tex]. Remember that dividing by a negative number reverses the inequality sign:
[tex]\[
-7x / -7 < 21 / -7
\][/tex]
[tex]\[
x < -3
\][/tex]
Therefore, the solution to the inequality [tex]\(-2x - 8 > 5x + 13\)[/tex] is [tex]\(\boxed{x < -3}\)[/tex].
This corresponds to choice A.
