Check and interpret the solution

Why check your answer?

Finding a value for x is not the final step! You must always check that this value does indeed satisfy the original problem statement, and answer the question using the correct units.

Method of checking

Substitute x with the value found into the original equation, and check that the equality holds true.

Example: for x = 12 and the equation 2 * x + 3 = 27, we calculate 2 * 12 + 3 = 24 + 3 = 27. The equality holds, so the solution is correct.

Answering the question in the problem

Note: the value of x is not always the final answer to the question! You must re-read the problem to find out what is actually being asked.

Example: “The perimeter of a rectangle is 30 cm. Its length is twice its width. What is the length?”

Let x = the width. The length is 2 * x. The perimeter is 2 * (length + width) = 30, so 2 * (2*x + x) = 30, which is 6 * x = 30, so x = 5. The width is 5 cm, but the question asked for the length: this is 2 × x = 10 cm.

Checking consistency with reality

A mathematically correct solution must also make sense in the context. A negative age, a negative length or a non-integer number of people are warning signs: you must then go back and check your equation.

A common pitfall to avoid

Never confuse the value of the unknown with the final answer required by the problem. Many pupils stop as soon as they find x, without re-reading the question. Always take the time to conclude with a full sentence and the appropriate unit, for example, ‘the length of the rectangle is 10 cm’.