Algebraic Operations: Multiplication and Division

We can multiply all the objects of the left hand side (LHS) of a balance scale by a number, and we must multiply all the objects on the right hand side (RHS) by the same number to preserve the equality (or balance) between the two sides. The balance scale below shows a tall cylindrical barrel containing water on the LHS and some gold colored weights on the RHS. The barrel is not full, and we need to determine the weight of a full barrel of water.

An equation is formed setting x="weight of a full barrel of water":

Exercise: Solve Two Step Problem

Solve the two step problem and show your working out clearly.

Summary

You can multiply or divide LHS and also the RHS when solving an equation which has a fractional value of x.