Ernest,

The challenge is to manipulate the equation, always maintaining the equality of the two sides, and end with the equation

b = some number.

The valid manipulations are to add the same amount to each side or multiply each side by the same amount.

In your equation

2b = 96 + b + 96 + ¹/₂ b

I want to put off working with fractions as long as possible so I would multiply both sides by 2. The equation then becomes

4b = 192 + 2b + 192 + b.

Next simplify the right side to get

4b = 384 + 3b

The goal is to have no "b term" on the right side so add -3b to each side to get

4b - 3b = 384 + 3b - 3b

so

b = 384.

Penny