Which of the [tex]\( q \)[/tex]-values satisfy the following inequality?

[tex]\[ 6 - 3q \leq 1 \][/tex]

Choose all answers that apply:

A. [tex]\( q = 0 \)[/tex]

B. [tex]\( q = 1 \)[/tex]

C. [tex]\( q = 2 \)[/tex]



Answer :

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]