Checking a Solution

To check a solution, put it back into the original equation, not into one of your later lines, and work out both sides separately. If they agree, the solution is right. For 7x - 4 = 3x + 8 and the answer x = 3: left side 7 × 3 - 4 = 17, right side 3 × 3 + 8 = 17. Agreed.

Checking catches arithmetic slips, and it catches something subtler: it tells the three kinds of outcome apart. A number that makes both sides agree is a solution. If no number can (3 = 5), there is no solution. If any number does (2 = 2), the equation is an identity.

Later in the journey, some moves (squaring both sides, multiplying by an expression) can invent answers that do not survive this test. Checking is how you catch them. Build the habit now, while it is cheap.