To solve the inequality [tex]\( 12x + 6 \geq 9x + 12 \)[/tex], follow these steps:
1. Simplify the inequality:
Start by subtracting [tex]\( 9x \)[/tex] from both sides of the inequality:
[tex]\[
12x + 6 - 9x \geq 12
\][/tex]
This simplifies to:
[tex]\[
3x + 6 \geq 12
\][/tex]
2. Isolate the variable:
Subtract 6 from both sides of the inequality to isolate the term with the variable [tex]\( x \)[/tex]:
[tex]\[
3x + 6 - 6 \geq 12 - 6
\][/tex]
Simplifying this gives:
[tex]\[
3x \geq 6
\][/tex]
3. Solve for [tex]\( x \)[/tex]:
Divide both sides by the coefficient of [tex]\( x \)[/tex], which is 3:
[tex]\[
\frac{3x}{3} \geq \frac{6}{3}
\][/tex]
This simplifies to:
[tex]\[
x \geq 2
\][/tex]
Therefore, the solution to the inequality [tex]\( 12x + 6 \geq 9x + 12 \)[/tex] is:
[tex]\[
x \geq 2
\][/tex]
Considering the options provided:
A. [tex]\( x \geq 2 \)[/tex]
B. [tex]\( x \geq 6 \)[/tex]
C. [tex]\( x \leq 6 \)[/tex]
D. [tex]\( x \leq 2 \)[/tex]
The correct answer is:
A. [tex]\( x \geq 2 \)[/tex]
