Checking a Solution

To check a solution, put it back into the original equation, not into one of your later lines. Work out each side separately. If the two sides agree, the solution is right. Take the equation 7x - 4 = 3x + 8 and the answer x = 3. The left side is 7 × 3 - 4 = 17. The right side is 3 × 3 + 8 = 17. Both sides give 17, so x = 3 is correct.

Checking catches arithmetic mistakes. It also tells the three kinds of outcome apart. A number that makes both sides agree is a solution. If the unknown cancels out and leaves a false statement, like 3 = 5, there is no solution. If it leaves a true statement, like 2 = 2, the equation is an identity.

Some operations can add extra answers that do not work. Squaring both sides can do this, and so can multiplying both sides by an expression that contains the unknown. Put each answer back into the original equation to check whether it is a real solution.