To solve the inequality [tex]\(-6x + 3 \geq 21\)[/tex], follow these steps:
1. Subtract 3 from both sides of the inequality:
[tex]\[
-6x + 3 - 3 \geq 21 - 3
\][/tex]
Simplifying this, we get:
[tex]\[
-6x \geq 18
\][/tex]
2. Divide both sides of the inequality by [tex]\(-6\)[/tex]:
When dividing both sides of an inequality by a negative number, the direction of the inequality sign must be flipped.
[tex]\[
x \leq \frac{18}{-6}
\][/tex]
Simplifying the right-hand side, we have:
[tex]\[
x \leq -3
\][/tex]
The correct solution to the inequality is [tex]\(x \leq -3\)[/tex], which corresponds to option A.
