The lesson
This lesson teaches Variables on Both Sides. Read each section in order, work through every example on paper, then use the practice problems and quick check at the bottom.
Get variables together
When you study get variables together, slow down and write one example in your notebook without looking at the screen. That active step is what turns reading into learning.
- 1Add or subtract to move all variable terms to one side.
- 2Move constants to the other side.
- 3Divide to isolate the variable.
Solve 2x + 3 = 5x - 6.
- 1Subtract 2x from both sides: 3 = 3x - 6.
- 2Add 6: 9 = 3x.
- 3Divide by 3: x = 3.
Why this matters
Variables on Both Sides shows up constantly in move variable terms to one side, then solve - and spot special cases. It also connects to what you will see on homework, quizzes, and the next unit in this grade.
Teachers often move fast in class. This page is here so you can pause, re-read, and practice until the idea feels familiar, not just until you have memorized a rule for one day.
Common mistakes to avoid
Rushing to the answer without writing steps. Middle-school math rewards clear work, and you catch errors earlier when steps are visible.
Mixing up similar ideas from the same topic. If two terms feel alike, make a two-column note: what is the same, what is different, and one example of each.
Key ideas from this lesson
- Get variables together
- Add or subtract to move all variable terms to one side.
- Move constants to the other side.
- Divide to isolate the variable.
Video walkthrough
Equations with Variables on Both Sides
Collect variable terms on one side, then solve.
Watch on YouTubeVariables on Both Sides (example)
Another worked example: 20 − 7x = 6x − 6.
Watch on YouTubePractice
For each problem: write your work in the box, type your answer, and check it. If you are stuck, reveal the solution one step at a time. Do not skip straight to the final answer.
Exercise 1
Try it yourselfSolve: 5x = 3x + 10.
Step-by-step solution
- 1Subtract 3x from both sides: 2x = 10.
- 2Divide by 2: x = 5.
- 3Check: 5(5) = 25 and 3(5) + 10 = 25 ✓.
Exercise 2
Try it yourselfSolve: 7x − 4 = 2x + 11.
Step-by-step solution
- 1Subtract 2x: 5x − 4 = 11.
- 2Add 4: 5x = 15.
- 3Divide by 5: x = 3.
Exercise 3
Try it yourselfSolve: 3(x + 2) = 2x + 9.
Step-by-step solution
- 1Distribute: 3x + 6 = 2x + 9.
- 2Subtract 2x: x + 6 = 9.
- 3Subtract 6: x = 3.
Exercise 4
Try it yourselfSolve: 2x + 4 = 2x + 7. How many solutions?
Step-by-step solution
- 1Subtract 2x from both sides: 4 = 7.
- 2This is false for every value of x.
- 3There is no solution.
Exercise 5
Try it yourselfSolve: 4(x − 1) = 4x − 4. How many solutions?
Step-by-step solution
- 1Distribute left side: 4x − 4 = 4x − 4.
- 2Subtract 4x: −4 = −4, always true.
- 3Infinitely many solutions.
Quick check
Answer all questions. Retake the quiz until you feel confident before moving on.
Variables on Both Sides
Question 1 of 4
Solve: 4x - 1 = 2x + 7.