To determine which [tex]\( q \)[/tex]-values satisfy the inequality [tex]\( 6 - 3q \leq 1 \)[/tex], we will solve this inequality step-by-step.
1. Start with the given inequality:
[tex]\[
6 - 3q \leq 1
\][/tex]
2. Subtract 6 from both sides to isolate the term involving [tex]\( q \)[/tex]:
[tex]\[
6 - 3q - 6 \leq 1 - 6
\][/tex]
Simplifying both sides, we get:
[tex]\[
-3q \leq -5
\][/tex]
3. Divide both sides of the inequality by [tex]\(-3\)[/tex]. Note that dividing by a negative number reverses the inequality sign:
[tex]\[
q \geq \frac{5}{3}
\][/tex]
This tells us that [tex]\( q \)[/tex] must be greater than or equal to [tex]\( \frac{5}{3} \)[/tex].
Now let's check each of the given [tex]\( q \)[/tex]-values against this condition:
- For [tex]\( q = 0 \)[/tex]:
[tex]\[
0 \geq \frac{5}{3}
\][/tex]
This is false because [tex]\( 0 \)[/tex] is not greater than or equal to [tex]\( \frac{5}{3} \)[/tex].
- For [tex]\( q = 1 \)[/tex]:
[tex]\[
1 \geq \frac{5}{3}
\][/tex]
This is also false because [tex]\( 1 \)[/tex] is not greater than or equal to [tex]\( \frac{5}{3} \)[/tex].
- For [tex]\( q = 2 \)[/tex]:
[tex]\[
2 \geq \frac{5}{3}
\][/tex]
This is true because [tex]\( 2 \)[/tex] is greater than [tex]\( \frac{5}{3} \)[/tex].
Since only [tex]\( q = 2 \)[/tex] satisfies the inequality, the correct answer is:
C) [tex]\( q = 2 \)[/tex]
