To solve the inequality [tex]\(3x - 9 \geq 27 - 6x\)[/tex], follow these detailed steps:
1. Start with the given inequality:
[tex]\[
3x - 9 \geq 27 - 6x
\][/tex]
2. Move all terms involving [tex]\(x\)[/tex] to one side of the inequality:
To simplify, add [tex]\(6x\)[/tex] to both sides of the inequality:
[tex]\[
3x - 9 + 6x \geq 27
\][/tex]
3. Combine like terms:
Combine the terms with [tex]\(x\)[/tex] on the left side:
[tex]\[
9x - 9 \geq 27
\][/tex]
4. Isolate the term with [tex]\(x\)[/tex]:
To isolate [tex]\(x\)[/tex], add [tex]\(9\)[/tex] to both sides of the inequality:
[tex]\[
9x - 9 + 9 \geq 27 + 9
\][/tex]
[tex]\[
9x \geq 36
\][/tex]
5. Solve for [tex]\(x\)[/tex] by dividing both sides by 9:
[tex]\[
\frac{9x}{9} \geq \frac{36}{9}
\][/tex]
[tex]\[
x \geq 4
\][/tex]
Therefore, the solution to the inequality [tex]\(3x - 9 \geq 27 - 6x\)[/tex] is [tex]\(x \geq 4\)[/tex].
So the correct answer choice is:
A. [tex]\( x \geq 4 \)[/tex]
