Solve multi-step equations
See this course’s project requirements
A checked algebra notebook that models four situations, solves equations and inequalities, and tests solutions against the original conditions.
Keep your working files in your own notebook or software. Save a private description, checklist, and work link in My Proof.
What to include
- Include four clearly defined quantity models with units.
- Show balanced transformations and distribution in at least one model.
- State a permitted inequality set and check its boundary.
- Check each final value in its original relationship.
- Add all six changed-case responses and explain one infeasible whole-number arrangement.
Review and revise
Use these criteria to check your work and choose what to improve.
- Method: applies the course-specific rules to the supplied cases with visible intermediate work.
- Accuracy: results agree with the stated facts, units, boundaries and independent checks.
- Reasoning: explains why the result follows and identifies a limitation or unresolved question.
- Transfer: completes changed cases and revises the final project when a relevant assumption changes.
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The idea in everyday life
Original case: 5x − 8 = 27; x is a number of identical model tokens.
Undo operations in reverse order while preserving equality. Keep each intermediate equation visible, and verify the proposed value in the original equation rather than only in the last line.
Solve multi-step equations — worked practice
Undo operations in reverse order while preserving equality. Keep each intermediate equation visible, and verify the proposed value in the original equation rather than only in the last line.
Original case: 5x − 8 = 27; x is a number of identical model tokens.
Case information
Paste at A1.
| ARecord | BGiven |
|---|---|
| Original case | Original case: 5x − 8 = 27; x is a number of identical model tokens. |
Copy as plain text
1. 1. Identify operations
Describe what happens to x before the result is 27.
You should see: x is multiplied by five, then eight is subtracted.
2. 2. Undo subtraction
Add eight to both sides.
You should see: 5x = 35.
3. 3. Undo multiplication
Divide both sides by five.
You should see: x = 7.
4. 4. Verify
Evaluate the original left side at seven.
You should see: 5 × 7 − 8 = 27; the equation is satisfied.
What to finish
A multi-step equation solution showing each inverse operation.
Watch for this
The original equation tests whether a transformation error occurred.
How can I tell I understand it?
Solve a changed two-operation equation without checking only the final line.
Quick knowledge check
Answer all 3 questions. Get at least 2 right and the lesson completes automatically.
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Answer all 3 questions above and get at least 2 right. You can review the explanations and try again.
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Source & access notes · checked 2026-10-01
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