Sure, let's solve the inequality step-by-step.
We are given the inequality:
[tex]\[ -4x < -12 \][/tex]
To isolate [tex]\( x \)[/tex], the goal is to get [tex]\( x \)[/tex] alone on one side of the inequality. The first step is to get rid of the coefficient of [tex]\( x \)[/tex], which is [tex]\(-4\)[/tex]. We do this by dividing both sides of the inequality by [tex]\(-4\)[/tex]. However, a crucial rule in inequalities is that when we divide (or multiply) both sides by a negative number, the direction of the inequality sign must be reversed.
Let's go through these steps:
1. Divide both sides of the inequality by [tex]\(-4\)[/tex]:
[tex]\[ \frac{-4x}{-4} > \frac{-12}{-4} \][/tex]
2. Simplify the left side and the right side:
[tex]\[ x > 3 \][/tex]
So, the solution to the inequality [tex]\( -4x < -12 \)[/tex] is:
[tex]\[ x > 3 \][/tex]
Therefore, the correct answer is:
[tex]\[ x > 3 \][/tex]
