Let's solve the inequality step by step:
Given the inequality:
[tex]\[ 12x + 6 \geq 9x + 12 \][/tex]
1. Subtract [tex]\(9x\)[/tex] from both sides:
[tex]\[ 12x + 6 - 9x \geq 9x + 12 - 9x \][/tex]
[tex]\[ 3x + 6 \geq 12 \][/tex]
2. Subtract 6 from both sides:
[tex]\[ 3x + 6 - 6 \geq 12 - 6 \][/tex]
[tex]\[ 3x \geq 6 \][/tex]
3. Divide both sides by 3:
[tex]\[ \frac{3x}{3} \geq \frac{6}{3} \][/tex]
[tex]\[ x \geq 2 \][/tex]
So, the solution to the inequality [tex]\(12x + 6 \geq 9x + 12\)[/tex] is:
[tex]\[ x \geq 2 \][/tex]
Hence, the correct answer is:
[tex]\[ \boxed{C. \, x \geq 2} \][/tex]
