Solving Equations

What will happen if you add or subtract an equal amount of weight on both sides of the scales? Solving equations is like balancing scales, we must always keep the sides equal.

Solving equations is just a matter of undoing operations that are being done to the variable. In a simple equation, this may mean that we only have to undo one operation, as in the following example.

Example 1

In an equation which has more than one operation, we have to undo the operations in the correct order. We start with the operation the farthest away from the variable.

Example 2

Example 3

Example 4

Example 5

Example 6

Example 7

Suppose there are variables on both sides of the equation. The trick now, is to get the variables on the same side by adding or subtracting them.

Example 8

Just watch what happens 6n + 17 = 5 + 4n 6n = – n 2n = – 12 – 17 – 4n ÷ 2 n = – 6 6n + 17 = 5 + 4n 6n + 12 = 4n 12 = – 2n – 5 – 6n ÷ – 2 n = – 6 6n + 17 = 5 + 4n 2n + 17 = 5 2n = – 12 – 4n – 17 ÷ 2 n = – 6 It doesn’t matter where you start

Example 9

Example 10

Example 11

Example 12

Example 13

Example 14

Example 15

Example 16

Example 17

Example 18