When we solve algebraic equations, our aim is to end up with one letter on one side of the equals sign and one number on the other. This is the solution.
We do this by using inverse operations to undo things that get in the way, but remember that we must do the same thing to both sides.
When brackets are involved, we multiply out the brackets first.
7(b + 3) - 2(b - 3) = 47
Multiply out each set of brackets.
7b + 21 - 2b + 6 = 47
Simplify by collecting like terms.
5b + 27 = 47
Subtract 27 from both sides.
5b + 27 - 27 = 47 - 27
5b = 20
Divide both sides by 5
5b ÷ 5 = 20 ÷ 5
b = 4