When x appears on both sides, first collect the x terms on one side. Subtract the smaller x term from both sides: 6x + 10 = 2x + 34 becomes 4x + 10 = 34.
Then solve as a two-step equation: 4x = 24, so x = 6. If there are brackets, expand them first: 4(x + 14) = 6(x + 3) becomes 4x + 56 = 6x + 18, then 38 = 2x and x = 19. Some equations have no solution, and some are true for every x.
Worked example
Solve 7x − 3 = 4x + 12
- Subtract 4x from both sides: 3x − 3 = 12.
- Add 3: 3x = 15, so divide by 3.
Answer:x = 5
Key words
- collect
- move like terms to one side
- balance
- do the same to both sides
- no solution
- an equation that can never be true
Practise this
New questions every time.
Common Core-referenced: 8.EE.C.7