To solve the inequality [tex]\(-6x + 3 \geq 21\)[/tex], follow these steps:
1. Isolate the variable term:
[tex]\[
-6x + 3 \geq 21
\][/tex]
Subtract 3 from both sides of the inequality:
[tex]\[
-6x \geq 21 - 3
\][/tex]
Simplify the right side:
[tex]\[
-6x \geq 18
\][/tex]
2. Solve for [tex]\(x\)[/tex]:
To solve for [tex]\(x\)[/tex], divide both sides by [tex]\(-6\)[/tex]. Remember, when dividing or multiplying both sides of an inequality by a negative number, the inequality sign flips:
[tex]\[
x \leq \frac{18}{-6}
\][/tex]
Simplify the fraction:
[tex]\[
x \leq -3
\][/tex]
Hence, the solution for the inequality [tex]\(-6x + 3 \geq 21\)[/tex] is [tex]\(x \leq -3\)[/tex].
Therefore, the correct answer is:
A. [tex]\(x \leq -3\)[/tex].
