Algebraic Manipulation Examples in Math
Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Algebraic Manipulation.
This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Math.
Concept Recap
Algebraic manipulation is the process of rewriting expressions or equations into equivalent forms to reveal structure or solve for unknowns.
It is like rearranging a sentence without changing its meaning.
Read the full concept explanation →How to Use These Examples
- Read the first worked example with the solution open so the structure is clear.
- Try the practice problems before revealing each solution.
- Use the related concepts and background knowledge badges if you feel stuck.
What to Focus On
Core idea: Algebraic manipulation changes the form of an expression without changing its value for any input variable.
Common stuck point: Every step must be an equivalence-preserving move — non-equivalent steps silently change the problem.
Sense of Study hint: After each step, substitute a test value to confirm both forms still match.
Worked Examples
Example 1
easySolution
- 1 Step 1: Distribute: 2x + 6 - x.
- 2 Step 2: Combine like terms: x + 6.
- 3 Check: At x = 1: 2(4) - 1 = 7 and 1 + 6 = 7 ✓
Answer
Example 2
mediumPractice Problems
Try these problems on your own first, then open the solution to compare your method.
Example 1
easyExample 2
mediumRelated Concepts
Background Knowledge
These ideas may be useful before you work through the harder examples.