Sure, let's solve the equation [tex]\(\frac{3a^2 - 1}{2b} = c\)[/tex] for [tex]\(b\)[/tex]. Here is a step-by-step solution:
1. Start with the given equation:
[tex]\[
\frac{3a^2 - 1}{2b} = c
\][/tex]
2. To isolate [tex]\(b\)[/tex], first eliminate the fraction by multiplying both sides of the equation by [tex]\(2b\)[/tex]:
[tex]\[
2b \cdot \frac{3a^2 - 1}{2b} = 2b \cdot c
\][/tex]
3. On the left side, the [tex]\(2b\)[/tex] in the numerator and denominator cancel out, leaving:
[tex]\[
3a^2 - 1 = 2bc
\][/tex]
4. Next, solve for [tex]\(b\)[/tex] by isolating it on one side of the equation. Divide both sides by [tex]\(2c\)[/tex]:
[tex]\[
b = \frac{3a^2 - 1}{2c}
\][/tex]
Therefore, the value of [tex]\(b\)[/tex] in terms of [tex]\(a\)[/tex] and [tex]\(c\)[/tex] is:
[tex]\[
b = \frac{3a^2 - 1}{2c}
\][/tex]
