NUMBAT OER - Open Educational Resources

2. Adding and subtracting

In the simple examples in the previous section, we established that we could do anything to an equation, so long as we did the same thing to both sides. In adding or subtracting, we simply did the same operation to each side of the equation, for instance:

x - 7 = 13
x - 7 + 7 = 13 + 7
x + 0 = 20

Adding 7 to both sides of the equation is designed to cancel out the -7 on the left-hand side of the equation. A simple way to shortcut this step is simply to move the -7 to the right-hand side of the equation and to change its sign. Thus:

x - 7 = 13
x = 13 + 7
x = 20

Similarly with an addition:

3x + 8 = 26
3x = 26 - 8
3x = 18