Equations with the unknown on both sides

When x appears twice

Some equations have the unknown x on both the left-hand side AND the right-hand side, for example:

5x + 2 = 2x + 14

We cannot solve this directly: we must first group all the x’s on one side, and all the numbers on the other side.

3-step method

Step	Action	Result
1	Subtract 2x from both sides	3x + 2 = 14
2	Subtract 2 from both sides	3x = 12
3	Divide both sides by 3	x = 4

We always group the unknowns on one side and the numbers on the other, in any order we like, as long as we follow the rules of equality.

Verification

We substitute x with 4 in the original equation:

• Left-hand side: 5 × 4 + 2 = 22
• Right-hand side: 2 × 4 + 14 = 22

Both sides are equal: x = 4 is indeed the solution.

Pitfall to avoid

When moving a term involving x to the other side of the equals sign, you must also change its sign, just as you would with a number. In 5x + 2 = 2x + 14, we subtract 2x (not add it) to make it disappear from the right-hand side. Forgetting to change the sign is the most common mistake in this type of equation.