Variables on Both Sides
Collect variable terms on one side first.
Key idea
Collect variable terms on one side first.
In depth
Move all variable terms to one side by adding or subtracting the same term from both sides, then solve as before. Choosing the side with the larger coefficient avoids negatives.
Worked example
5x − 4 = 2x + 11: subtract 2x → 3x − 4 = 11; add 4 → 3x = 15; x = 5.
Formula
Real-world uses
- Comparing two phone plans to find the break-even number of minutes
Common mistake
Moving a term without changing its sign.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Variables on Both Sides?
Collect variable terms on one side first. It is a topic at the intermediate level in Algebra.
What is the formula for Variables on Both Sides?
The key formula is 3x+2 = x+10.
Where is Variables on Both Sides used in real life?
Real-world examples: Comparing two phone plans to find the break-even number of minutes.
What should I learn before Variables on Both Sides?
Make sure you are comfortable with Multi-Step Equations, the previous topic in Algebra.
What is a common mistake with Variables on Both Sides?
Moving a term without changing its sign.
How can I practise Variables on Both Sides?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Variables on Both Sides?
Move on to Literal Equations next.
Related intermediate topics in Algebra
- Multi-Step Equations – Distribute, combine like terms, move variables to one side.
- Literal Equations – Rearrange formulas to solve for a chosen variable.
- Identity and No-Solution Equations – Some equations are always true or never true.
- Linear Inequalities – Solve like equations but reverse the sign when multiplying by a negative.
- Compound Inequalities – Combine two inequalities using “and” or “or”.
- Absolute Value Equations – Split into two cases: inside equals ± the value.