Solve and interpret an inequality
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: A box holds at most 25 tokens. Four labels are fixed and each group adds three tokens: 3x+4 ≤ 25, with x a nonnegative whole number.
An inequality describes a set of permitted values. Addition and subtraction preserve its direction. Multiplying or dividing by a negative reverses the comparison. A context may further restrict values to whole numbers or nonnegative quantities.
Solve and interpret an inequality — worked practice
An inequality describes a set of permitted values. Addition and subtraction preserve its direction. Multiplying or dividing by a negative reverses the comparison. A context may further restrict values to whole numbers or nonnegative quantities.
Original case: A box holds at most 25 tokens. Four labels are fixed and each group adds three tokens: 3x+4 ≤ 25, with x a nonnegative whole number.
Case information
Paste at A1.
| ARecord | BGiven |
|---|---|
| Original case | Original case: A box holds at most 25 tokens. Four labels are fixed and each group adds three tokens: 3x+4 ≤ 25, with x a nonnegative whole number. |
Copy as plain text
1. 1. Isolate the variable expression
Subtract four from both sides.
You should see: 3x ≤ 21.
2. 2. Divide and state the set
Divide by positive three and include the original whole-number condition.
You should see: x ≤ 7; permitted groups are 0,1,2,3,4,5,6,7.
3. 3. Test boundary and violation
Check seven and eight in the original capacity expression.
You should see: Seven gives 25 and fits; eight gives 28 and does not fit.
4. 4. Test a negative coefficient
Solve −2z < −6 and explain the comparison reversal.
You should see: z > 3, because division by −2 reverses the inequality.
What to finish
A solution set, boundary tests and negative-coefficient comparison.
Watch for this
The context restricts x to a nonnegative whole number.
How can I tell I understand it?
Distinguish a numerical solution set from feasible group counts and reverse comparisons when dividing by a negative.
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