Solving One-Step Equations

An equation is a balance. Whatever you do to one side, do to the other, and it stays level.

Undo what was done

n + 4 = 9 has 4 added, so subtract 4 from both sides. That leaves n = 5.

The same for multiplying

5n = 30 has n multiplied by 5, so divide both sides by 5, giving n = 6.

Always check

Put the answer back into the original. If both sides match, it is right.

An equation is a balance

The equals sign says both sides weigh the same. Whatever you do to one side you must do to the other, or the balance tips and the equation stops being true. That single principle is the whole method for solving equations.

Undo with the inverse operation

To solve n + 3 = 8, subtract 3 from both sides: n = 5. To solve 4n = 20, divide both sides by 4: n = 5. Each operation is undone by its inverse, which is why addition and subtraction, and multiplication and division, are learned in pairs.

Show what you did to both sides

Write the subtraction under both sides rather than doing it in your head. When equations get longer, working that shows each step is checkable and correctable; working that jumps to an answer is neither.

Always substitute back

4n = 20 giving n = 5 checks out because 4 × 5 = 20. Substituting into the original equation — not the rearranged one — catches an error made at any step. It takes five seconds and it is the only complete check there is.