Consider the function represented by the equation [tex]\(6q = 3s - 9\)[/tex]. Write the equation in terms of the independent variable [tex]\(q\)[/tex].

A. [tex]\(f(q) = \frac{1}{2} q - \frac{3}{2}\)[/tex]

B. [tex]\(f(q) = 2s + 3\)[/tex]

C. [tex]\(f(5) = \frac{1}{2} \cdot 5 - \frac{3}{2}\)[/tex]

D. [tex]\(f(q) = 2q + 3\)[/tex]



Answer :

To write the equation [tex]\(6q = 3s - 9\)[/tex] in terms of the independent variable [tex]\(q\)[/tex], follow these steps:

1. Start with the given equation:
[tex]\[ 6q = 3s - 9 \][/tex]

2. Isolate the term involving [tex]\(s\)[/tex] on one side of the equation. To do this, add 9 to both sides of the equation:
[tex]\[ 6q + 9 = 3s \][/tex]

3. Solve for [tex]\(s\)[/tex] by dividing both sides of the equation by 3:
[tex]\[ s = \frac{6q + 9}{3} \][/tex]

4. Simplify the right side of the equation:
[tex]\[ s = \frac{6q}{3} + \frac{9}{3} \][/tex]
[tex]\[ s = 2q + 3 \][/tex]

Therefore, the equation in terms of the independent variable [tex]\(q\)[/tex] is:
[tex]\[ f(q) = 2q + 3 \][/tex]

None of the other given options are correct. Thus, the correct function is:
[tex]\[ f(q) = 2q + 3 \][/tex]