One-Step Equations (Multiply / Divide)

Divide when the variable is multiplied

In $4x = 28$, the $4$ is a coefficient — it multiplies the variable. To reverse a multiplication by $4$, divide both sides by $4$. The left side becomes just $x$, and the right side becomes $28 \div 4 = 7$.

Divide by the number attached to the variable, nothing else. If the equation is $9x = 45$, divide both sides by $9$ and the answer is $x = 5$.

Multiply when the variable is divided

In $\dfrac{x}{5} = 3$, the variable is divided by $5$. Reverse it: multiply both sides by $5$. The left side becomes $x$, and the right side becomes $3 \cdot 5 = 15$.

A fraction bar means division, so $\dfrac{x}{5}$ is the same as $x \div 5$. Whenever the variable sits on top of a fraction with a plain number underneath, multiplying both sides by that number clears it in one move.

Watch the signs

Negative numbers follow the same steps — you just have to track the sign. In $-6x = 42$, divide both sides by $-6$, the whole coefficient including its sign. A positive divided by a negative is negative, so $x = -7$.

The same care applies when multiplying: in $\dfrac{x}{-5} = 4$, multiply both sides by $-5$ to get $x = -20$.

Worked examples

Try one yourself

Common questions