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Answer :
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).
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).
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