What is the solution to this inequality?

[tex]\[ -13x \ \textgreater \ -39 \][/tex]

A. [tex]\[ x \ \textless \ 3 \][/tex]

B. [tex]\[ x \ \textgreater \ 3 \][/tex]

C. [tex]\[ x \ \textless \ -3 \][/tex]

D. [tex]\[ x \ \textgreater \ -3 \][/tex]



Answer :

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].