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Solve for [tex]$x$[/tex]:

[tex]-4x \ \textless \ -12[/tex]

A. [tex]x \ \textgreater \ 3[/tex]
B. [tex]x \ \textless \ 3[/tex]
C. [tex]x \ \textgreater \ -3[/tex]
D. [tex]x \ \textless \ -3[/tex]

Sagot :

GinnyAnsweridn
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]
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