Some equations multiply or divide the variable instead of adding to it. The balance idea from One-Step Equations with Adding and Subtracting still works: do the same thing to both sides.
Idea clave
To undo multiplying by a number, divide both sides by it. To undo dividing by a number, multiply both sides by it. $4x = 12$ becomes $x = 12 \div 4 = 3$.
Por qué funciona
$4x = 12$ says four equal bags weigh 12. Split each side into 4 equal groups and keep one group from each: one bag on the left, 3 cubes on the right. Still balanced. Dividing by 4 undoes multiplying by 4, because $4x \div 4 = x$.
Ejemplo resuelto: Undo multiplying
Solve $4x = 12$.
- Divide both sides by 4: $x = 12 \div 4$.
- $x = 3$. Check: $4 \times 3 = 12$.
Respuesta: $x = 3$
Ejemplo resuelto: Undo dividing
Solve $\frac{m}{5} = 7$.
- Multiply both sides by 5: $m = 7 \times 5$.
- $m = 35$. Check: $35 \div 5 = 7$.
Respuesta: $m = 35$
Ejemplo resuelto: A fraction coefficient
Solve $\frac{2}{3}k = 10$.
- Multiply both sides by the reciprocal, $\frac{3}{2}$ (that is the same as dividing by $\frac{2}{3}$).
- $k = 10 \times \frac{3}{2} = 15$.
- Check: $\frac{2}{3} \times 15 = 10$.
Respuesta: $k = 15$
Ejemplo resuelto: A decimal coefficient
Solve $0.4w = 3.2$.
- Divide both sides by 0.4: $w = 3.2 \div 0.4$.
- Multiply both numbers by 10: $32 \div 4 = 8$.
- Check: $0.4 \times 8 = 3.2$.
Respuesta: $w = 8$
Error común
Subtracting the coefficient: solving $4x = 12$ as $x = 12 - 4 = 8$. The 4 is multiplying $x$, not added to it. Quick check: $4x$ means $4 \times x$, and $4 \times 8 = 32$, not 12.