To solve the inequality [tex]\( -13x > -39 \)[/tex], we need to isolate [tex]\( x \)[/tex] by performing algebraic operations. Here are the steps:
1. Divide both sides by -13:
In order to isolate [tex]\( x \)[/tex], divide both sides of the inequality by -13. Don't forget that dividing by a negative number reverses the direction of the inequality. So, we have:
[tex]\[
x < \frac{-39}{-13}
\][/tex]
2. Simplify the right-hand side:
Now, simplify the fraction on the right-hand side. The fraction [tex]\(\frac{-39}{-13}\)[/tex] simplifies to [tex]\(3\)[/tex]. Therefore, the inequality becomes:
[tex]\[
x < 3
\][/tex]
So the correct solution to the inequality [tex]\( -13x > -39 \)[/tex] is:
[tex]\[
x < 3
\][/tex]
Therefore, the answer is [tex]\( \boxed{A} \)[/tex] [tex]\( x < 3 \)[/tex].
