Keep equations balanced
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.
Want more background?
The idea in everyday life
Original case: x + 7 = 19. A second equation is 4y = 28.
An equation is a balance. Applying the same addition, subtraction, multiplication or nonzero division to both sides preserves its solutions. A term does not magically change sign; the operation must be applied to both sides.
Keep equations balanced — worked practice
An equation is a balance. Applying the same addition, subtraction, multiplication or nonzero division to both sides preserves its solutions. A term does not magically change sign; the operation must be applied to both sides.
Original case: x + 7 = 19. A second equation is 4y = 28.
Case information
Paste at A1.
| ARecord | BGiven |
|---|---|
| Original case | Original case: x + 7 = 19. A second equation is 4y = 28. |
Copy as plain text
1. 1. Undo addition
Subtract seven from both sides of the first equation.
You should see: x + 7 − 7 = 19 − 7, so x = 12.
2. 2. Undo multiplication
Divide both sides of the second equation by four.
You should see: 4y ÷ 4 = 28 ÷ 4, so y = 7.
3. 3. Substitute
Check both values in the equations before any transformation.
You should see: 12 + 7 = 19 and 4 × 7 = 28.
4. 4. Explain preservation
Describe why subtracting only from the left would fail.
You should see: Changing only one side would generally destroy equality.
What to finish
Two balanced solution chains with original-equation checks.
Watch for this
Both sides become zero, so values that did not solve the original equation can now satisfy the new one.
How can I tell I understand it?
Choose an inverse operation and preserve equality without losing the original constraint.
Quick knowledge check
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