Solve the following equation: 4x + 7 = 2x - 5

Some students struggle to solve equations with unknowns on both sides. I think the easiest way to solve these types of equations is to use the balance method. This is where you treat the equation like a weighing scale where whatever maths operation you do to one side, you must also do to the other side in order to keep the equation balanced. So with our equation the sensible first step is to take away 2x from both sides. So the left hand side of the equation becomes 2x + 7 and the right hand side of the equation becomes -5 (watch out! a common mistake is to forget to write the - sign). So our working so far should look like this: 4x + 7 = 2x - 5, 2x + 7 = -5 Our next step should be to get rid of the + 7 on the left hand side of the equation. So we should subtract 7 from both sides. This leaves us with 2x on the left hand side of the equation and - 12 on the right hand side (watch out! -5 - 7 = -12 be careful not to make a mistake when doing this subtraction) So our working should now look like this: 4x + 7 = 2x - 5, 2x + 7 = -5, 2x = - 12 The final step is to divide both sides of the equation by 2. This is because 2x divided by 2 gives us x (which is what we are trying to find when solving this equation). On the right hand side of the equation we get-12 divided by 2 = -6. So our answer is x = -6. The full solution should look like this: 4x + 7 = 2x - 5, 2x + 7 = -5, 2x = - 12, x = -6