Unit 2 · Topic 2

Variables on Both Sides

Overview

Move variable terms to one side, then solve - and spot special cases.

Topic 2 of 2~24 min
All units
Unit overview

The lesson

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

  1. 1Add or subtract to move all variable terms to one side.
  2. 2Move constants to the other side.
  3. 3Divide to isolate the variable.
Worked example

Solve 2x + 3 = 5x - 6.

  1. 1Subtract 2x from both sides: 3 = 3x - 6.
  2. 2Add 6: 9 = 3x.
  3. 3Divide by 3: x = 3.

Why this matters

Move variable terms to one side, then solve - and spot special cases.

These ideas show up on homework, quizzes, and the next unit in this grade. Getting comfortable here saves time later when the problems stack more steps together.

Common mistakes to avoid

Rushing to the answer without writing steps. Clear work helps you catch mistakes and shows your reasoning.

Re-reading the question too quickly. Underline what you are solving for before you start calculating.

Key ideas from this lesson

  1. Get variables together
  2. Add or subtract to move all variable terms to one side.
  3. Move constants to the other side.
  4. Divide to isolate the variable.

Video walkthroughs

Khan Academy

Equations with Variables on Both Sides

Collect variable terms on one side, then solve.

Watch on YouTube
Khan Academy

Variables on Both Sides (example)

Another worked example: 20 − 7x = 6x − 6.

Watch on YouTube
Math Antics

Solving 2-Step Equations

Collect like terms as a step toward variables on both sides.

Watch on YouTube
Math Antics

Solving Basic Equations

Isolate the variable when terms appear on both sides.

Watch on YouTube

Practice

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 yourself

Solve: 5x = 3x + 10.

Step-by-step solution

  1. 1Subtract 3x from both sides: 2x = 10.
  2. 2Divide by 2: x = 5.
  3. 3Check: 5(5) = 25 and 3(5) + 10 = 25 ✓.

Exercise 2

Try it yourself

Solve: 7x − 4 = 2x + 11.

Step-by-step solution

  1. 1Subtract 2x: 5x − 4 = 11.
  2. 2Add 4: 5x = 15.
  3. 3Divide by 5: x = 3.

Exercise 3

Try it yourself

Solve: 3(x + 2) = 2x + 9.

Step-by-step solution

  1. 1Distribute: 3x + 6 = 2x + 9.
  2. 2Subtract 2x: x + 6 = 9.
  3. 3Subtract 6: x = 3.

Exercise 4

Try it yourself

Solve: 2x + 4 = 2x + 7. How many solutions?

Step-by-step solution

  1. 1Subtract 2x from both sides: 4 = 7.
  2. 2This is false for every value of x.
  3. 3There is no solution.

Exercise 5

Try it yourself

Solve: 4(x − 1) = 4x − 4. How many solutions?

Step-by-step solution

  1. 1Distribute left side: 4x − 4 = 4x − 4.
  2. 2Subtract 4x: −4 = −4, always true.
  3. 3Infinitely many solutions.

Re-read the lesson section if you get stuck, then try again without peeking at the solution.

Khan Academy

Variables on both sides

Open resource
Math Worksheets 4 Kids

Equation worksheets

Open resource

Quick check

Answer all questions. Retake the quiz until you feel confident before moving on.

Variables on Both Sides

Question 1 of 4

Medium

Solve: 4x - 1 = 2x + 7.

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