Question

what is the value of b in the equation $\frac{12}{4 + b}=\frac{4}{4b + 2}$? b = 11 b = $\frac{11}{2}$ b = $\frac{1}{4}$ b = 4

Explanation:

Step1: Cross - multiply the equation

Given $\frac{12}{4 + b}=\frac{4}{4b + 2}$, we get $12(4b + 2)=4(4 + b)$.

Step2: Expand both sides

$12\times4b+12\times2 = 4\times4+4\times b$, which simplifies to $48b+24 = 16 + 4b$.

Step3: Move terms with b to one side

Subtract $4b$ from both sides and subtract 24 from both sides: $48b-4b=16 - 24$.

Step4: Combine like terms

$44b=-8$.

Step5: Solve for b

$b =-\frac{8}{44}=-\frac{2}{11}$.

Answer:

$b =-\frac{2}{11}$