One-Step Equations (Add / Subtract)

The one move: use the opposite operation

Look at what is being done to the variable, then do the opposite to both sides. The opposite of adding is subtracting, and the opposite of subtracting is adding. The opposite of multiplying is dividing, and the opposite of dividing is multiplying.

So in $x + 7 = 12$, the equation adds $7$ — you subtract $7$ from both sides. In $4m = 28$, the variable is multiplied by $4$ — you divide both sides by $4$. One move, and the variable is alone.

Whatever you do to one side, you must do to the other. An equation is a balance: the same move on both sides keeps it balanced, and that's what makes the answer valid.

Reading the equation correctly

The most common early mistake is misreading which operation is happening. $x + 6$ means $6$ is added. $x - 4$ means $4$ is subtracted. $3x$ means $x$ is multiplied by $3$ — no symbol between a number and a variable always means multiplication. And $\dfrac{x}{5}$ means $x$ is divided by $5$.

Once you name the operation out loud — "$x$ is being multiplied by $3$" — the move that solves it is automatic: divide both sides by $3$.

Negative answers are normal

Don't panic if the answer comes out negative. In $x + 9 = 4$, subtracting $9$ from both sides gives $x = -5$ — a perfectly good answer. Check it: $-5 + 9 = 4$. If your last move divides by a negative number, slow down and track the sign: $-5x = 35$ gives $x = -7$, not $7$.

Worked examples

Try one yourself

Common questions