In $3x + 5 = 20$, two things happened to $x$: it was multiplied by 3, and then 5 was added. You know how to undo each one from one-step equations. The question is the order.
Idea clave
Undo the steps in reverse order: first undo the adding or subtracting, then undo the multiplying or dividing. Do each step to the whole of both sides.
Por qué funciona
Getting dressed, you put on socks, then shoes. Undressing, you take off the shoes first. Here $x$ was multiplied first and the 5 was added last, so the 5 comes off first. You could divide first, but then every term must be divided, $x + \frac{5}{3} = \frac{20}{3}$, which is correct but messier.
Worked examples
Ejemplo resuelto: Positive numbers
Solve $3x + 5 = 20$.
- Subtract 5 from both sides: $3x = 15$.
- Divide both sides by 3: $x = 5$.
- Check: $3(5) + 5 = 20$ ✓.
Respuesta: $x = 5$
Ejemplo resuelto: Negative numbers
Solve $-4x - 7 = 13$.
- Add 7 to both sides: $-4x = 20$.
- Divide by $-4$: $x = -5$.
- Check: $-4(-5) - 7 = 20 - 7 = 13$ ✓.
Respuesta: $x = -5$
Ejemplo resuelto: Dividing instead of multiplying
Solve $\frac{x}{5} + 3 = -1$.
- Subtract 3: $\frac{x}{5} = -4$.
- Multiply by 5: $x = -20$.
- Check: $-20 \div 5 + 3 = -4 + 3 = -1$ ✓.
Respuesta: $x = -20$
Error común
Dividing only part of a side: from $3x + 5 = 20$ writing $x + 5 = \frac{20}{3}$. If you divide, you must divide every term. Safer: undo the $+5$ first. Always check by substituting your answer into the original equation.