We can solve equations with letters by getting rid of whatever is next to the letter on the left side of the equal sign so that the letter is on it’s own.
But we can’t just get rid of what’s on the left without doing the same thing to what’s on the right of the equal sign.
“Doing the same to both sides” of the equal sign is the key to solving equations,
“Doing The Same To Both Sides”
The examples below illustrate the very important concept of “doing the same to both sides” of an equation.
| Left | Right | |
| 5 apples = 5 apples |  |
|
| Take away 2 apples from both sides |  |
|
| 3 apples = 3 apples
Both sides are still equal |
 |
|
It’s quite straightforward. Let’s do the same thing to both sides with some more apples.
| Left | Right | |
| n + 3 apples = 7 apples |  |
|
| Take away 3 apples from both sides |  |
|
| n = 4 applesBoth sides are still equal and now we know what n equals. | n |  |
If two things are equal and you do exactly the same thing to both things, they will still be equal.
Examples of solving equations by subtracting from both sides
Here are more examples – this time with no apples!
| Problem | Solution |
| n + 6 = 14 | |
| Take 6 away from both sides to leave n on the left | n + 6 – 6 = 14 – 6 n + 0 = 8 n = 8 |
| Problem | Solution |
| a + 23 = 64 | |
| Take 23 away from both sides to leave a on the left | a + 23 – 23 = 64 – 23 a + 0 = 41 a = 41 |
Discuss with your children the concept of “doing the same thing to both sides.” Use examples from real life.
e.g. “If you and your brother both had $10 you would have equal amounts. Correct? If I gave you both and additional $2, how much would you both have? Would it still be equal?”
Recap
We can use the following steps to solve many equations:
| The letter represents the number that we want to find. | a + 12 = 47 |
| We want to get the letter on its own on the left side of the = sign | a = |
| We can get rid of whatever is next to the letter – as long as whatever we do to get rid of it is also done on the other side. | a + 12 – 12 = 47 – 12 a = 35 |
Examples of solving equations by adding to both sides
We’ve seen how to “get rid of” of positive numbers on the left by subtracting them from both sides of the equation. In the examples below we’ll see how to “get rid” of negative values by adding to both sides.
| Problem | Solution |
| n – 5 = 12 | |
| Add 5 to both sides to leave n on the left | n – 5 + 5 = 12 + 5 n + 0 = 17 n = 17 |
| Problem | Solution |
| a – 42 = 16 | |
| Add 42 to both sides to leave a on the left | a – 42 + 42 = 16 + 42 a + 0 = 58 a = 58 |
You can practice solving equations like the examples on this page by using the four worksheets below
- Equations with addition e.g. n + 4 = 11
- Equations with subtraction e.g. x – 4 = 2
- Subtraction and addition equations (1 of 2) e.g. a + 3 = 7 and x – 9 = 11
- Subtraction and addition equations (2 of 2) e.g. a + 3 = 7 and x – 9 = 11
You’ll find a listing of these and more solving equations worksheets here.
