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------------------------------------------------ Which of the following represents the solution to the inequality [tex]4x - 12 < 6x + 6[/tex]?

A. [tex]x < -9[/tex]

B. [tex]x > -9[/tex]

C. [tex]x < 9[/tex]

D. [tex]x > 9[/tex]

To solve the inequality [tex]$4x - 12 < 6x + 6$[/tex], we can follow these steps:

1. Move the terms involving [tex]$x$[/tex] to one side:
We start by subtracting [tex]$6x$[/tex] from both sides to get the [tex]$x$[/tex]-terms together.

[tex]\[
4x - 6x - 12 < 6
\][/tex]

2. Simplify the equation:
Combine the [tex]$x$[/tex]-terms:

[tex]\[
-2x - 12 < 6
\][/tex]

3. Isolate the [tex]$x$[/tex]-term:
Add 12 to both sides to move the constant term to the right side of the inequality:

[tex]\[
-2x < 18
\][/tex]

4. Solve for [tex]$x$[/tex]:
Divide both sides of the inequality by [tex]$-2$[/tex]. Remember, dividing or multiplying both sides of an inequality by a negative number reverses the inequality sign.

[tex]\[
x > -9
\][/tex]

Therefore, the solution to the inequality is [tex]$x > -9$[/tex], which corresponds to option (B).