Solving simple equations

Simple equations are equations those have just one variable and which can be solved by using very algebraic operations. At times, you can even solve them mentally. These are also called one step equations because in one step. Since they involve variables and need to perform algebraic operations for solutions, they are also referred as algebra simple equations.

In many cases the one step equations are based on word problems and those are framed as per the statement of the word problem. Let us illustrate a few examples to understand how to solve simple equations.

Let x + 1 = 5. The solution is to find the value of x. We see on the left side a 1 is added to the variable. So to isolate that, we need to undo that addition by the inverse algebraic operation, which is subtraction. Since 1 is added to the variable, in the undoing process we need to subtract 1 on the left side. But since this is an equation doing any operation only on one side is prohibited since the balance of the equation is disturbed. Hence to maintain the balance a 1 must also be subtracted on the right side.

So the method of solution is (x + 1) – 1 = 5 – 1, or, x = 4, which is the solution. The solution can be checked by plugging that value in the original equation. That is, if x = 4, then the left side becomes as, x + 1 = 4 +1 = 5 = right side. Hence the solution is correct.

Let x – 3 = 4. Here the undoing operation is ‘add 3’ on both sides. So, (x – 3) +3 = 4 + 3, or, x = 7 which is the solution.
Next let us the equation 3x = 9. In this case, the variable is multiplied by 3 on the left side. In this case, the undoing operation is ‘divide by 3’ on both sides. So, (3x/3) = (9/3) or, x = 3, which is the solution. Similarly the undoing operation for a division is ‘multiply by the same number’ on both sides. For example, if, (x/2) = 4, then, (x/2)*2 = 4*2 or, x = 8.

Let us see how one step equations are formed from word problems.
‘Ben is 5 years older than Joan and Joan is 3 year old. How old is Ben?’ Let ‘x’ be the age of Ben. Since he is 5 years older that Joan, the equation is x – 5 = 3 and the solution is x – 5 + 5 = 3 + 5 or x = 8. Hence Ben is 8 years old.