To solve the inequality [tex]\( -9x < 63 \)[/tex], let's follow a step-by-step process:
1. Start with the given inequality:
[tex]\[
-9x < 63
\][/tex]
2. Isolate [tex]\( x \)[/tex] by dividing both sides of the inequality by [tex]\(-9\)[/tex]:
When you divide both sides of an inequality by a negative number, the direction of the inequality changes.
[tex]\[
\frac{-9x}{-9} > \frac{63}{-9}
\][/tex]
3. Simplify both sides:
[tex]\[
x > -7
\][/tex]
4. Interpret and choose the correct answer:
From the steps above, we have determined that [tex]\( x \)[/tex] must be greater than [tex]\(-7\)[/tex]. Among the given multiple-choice options, the correct answer is:
[tex]\[
x > -7
\][/tex]
Thus, the correct answer is:
[tex]\[
x > -7
\][/tex]
