Handle brackets and like terms
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.
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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: 2(x + 3) + x = 21.
Distribution multiplies every term inside a bracket. Like terms have the same variable part; their coefficients may be combined. Do not combine a variable term with a constant as if they measured the same thing.
Handle brackets and like terms — worked practice
Distribution multiplies every term inside a bracket. Like terms have the same variable part; their coefficients may be combined. Do not combine a variable term with a constant as if they measured the same thing.
Original case: 2(x + 3) + x = 21.
Case information
Paste at A1.
| ARecord | BGiven |
|---|---|
| Original case | Original case: 2(x + 3) + x = 21. |
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1. 1. Distribute
Multiply both bracket terms by two.
You should see: 2x + 6 + x = 21.
2. 2. Combine like terms
Add the coefficients of x while leaving six separate.
You should see: 3x + 6 = 21.
3. 3. Solve
Subtract six, then divide by three.
You should see: 3x = 15; x = 5.
4. 4. Check distribution
Substitute five into the bracketed original expression.
You should see: 2(5+3)+5 = 16+5 = 21.
What to finish
A bracket expansion, simplified equation and checked solution.
Watch for this
Distribution applies to every term, so the result is 2x+6.
How can I tell I understand it?
Expand and solve a changed expression while explaining why terms may combine.
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