Question

If $b=6-\left(\frac{4b+3}{2a-5}\right)$, express $a$ in terms of $b$.

• A. $a=\frac{33-b}{2(b-6)}$
• B. $a=\frac{33-b}{2(6-b)}$
• C. $a=\frac{33+b}{2(6+b)}$
• D. $a=\frac{33-b}{2(6+b)}$

Answer 1

The correct option is B $a=\frac{33-b}{2(6-b)}$

Given, $b=6-\left(\frac{4b+3}{2a-5}\right)$
Multiply by $(2a-5)$ both sides
$b(2a-5)=6(2a-5)-(4a+3)$
$2ab-5b=12a-30-4b-3$
$2ab-12a=5b-30-4b-3$
$2a(b-6)=b-33$

$\therefore a=\frac{b-33}{2(b-6)}$