You can check a solution by substituting. Now you will find it. Think of the equation as a balance: both sides weigh the same.
Idea clave
To undo adding a number, subtract it from both sides. To undo subtracting a number, add it to both sides. $x + 5 = 12$ becomes $x = 12 - 5 = 7$.
Por qué funciona
If two amounts are equal and you take 5 away from each, they are still equal. Take 5 from only one side and the scale tips: the sides are no longer equal. Subtracting 5 is the right move because it undoes adding 5: $(x + 5) - 5 = x$, which leaves $x$ alone on its side.
Ejemplo resuelto: Undo adding
Solve $x + 5 = 12$.
- Subtract 5 from both sides: $x + 5 - 5 = 12 - 5$.
- $x = 7$.
- Check: $7 + 5 = 12$.
Respuesta: $x = 7$
Ejemplo resuelto: Undo subtracting
Solve $n - 3.5 = 8.2$.
- Add 3.5 to both sides: $n = 8.2 + 3.5$.
- $n = 11.7$.
- Check: $11.7 - 3.5 = 8.2$.
Respuesta: $n = 11.7$
Ejemplo resuelto: With fractions
Solve $\frac{2}{3} + y = \frac{5}{4}$.
- Subtract $\frac{2}{3}$ from both sides: $y = \frac{5}{4} - \frac{2}{3}$.
- Common denominator 12: $\frac{15}{12} - \frac{8}{12} = \frac{7}{12}$.
- Check: $\frac{8}{12} + \frac{7}{12} = \frac{15}{12} = \frac{5}{4}$.
Respuesta: $y = \frac{7}{12}$
Error común
Subtracting on one side only, or adding when you should subtract. For $x + 5 = 12$, writing $x = 12 + 5 = 17$ undoes nothing. Quick check: substitute your answer. $17 + 5 = 22$, not 12, so it is wrong; $7 + 5 = 12$ is right.