Card 1 of 20
EasyStudy card 1
Prompt
Which inequality phrase corresponds to ‘at least’?
The boundary is included.
Answer
Greater than or equal to, \(\ge\).
Example
At least \(20\) means \(x\ge20\).
MathChapter 5: Word Problems in Real-Life Situations
Flashcards
Solving Word Problems Using Inequalities Flashcards
Twenty focused cards on constraint language, budgets, sign reversal, integer interpretation, pricing comparisons, and verification.
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Session progress0 of 20 studied
Card 1 of 20. Answer hidden.
Card 2 of 20
EasyStudy card 2
Prompt
Which inequality phrase corresponds to ‘at most’?
It gives a maximum.
Answer
Less than or equal to, \(\le\).
Example
At most \(12\) means \(x\le12\).
Card 3 of 20
EasyStudy card 3
Prompt
What does ‘no more than \(a\)’ mean?
Exactly \(a\) is allowed.
Answer
The quantity is \(\le a\).
Example
A load no more than \(50\) kg satisfies \(m\le50\).
Card 4 of 20
EasyStudy card 4
Prompt
What does ‘fewer than \(a\)’ mean?
The boundary is excluded.
Answer
The quantity is \(<a\).
Example
Fewer than \(30\) items means \(n<30\).
Card 5 of 20
EasyStudy card 5
Prompt
What does ‘no less than \(a\)’ mean?
It cannot fall below the boundary.
Answer
The quantity is \(\ge a\).
Example
No less than \(8\) hours means \(h\ge8\).
Card 6 of 20
MediumStudy card 6
Prompt
How is a maximum budget translated?
A maximum allows equality.
Answer
The total-cost expression is less than or equal to the budget.
Example
\(40+6x\le160\).
Card 7 of 20
MediumStudy card 7
Prompt
How is a minimum revenue target translated?
A minimum allows equality.
Answer
The revenue or earnings expression is greater than or equal to the target.
Example
\(15n-90\ge300\).
Card 8 of 20
MediumStudy card 8
Prompt
When does an inequality sign reverse while solving?
Addition and subtraction do not reverse it.
Answer
When both sides are multiplied or divided by a negative number.
Example
From \(-5x\ge20\), obtain \(x\le-4\).
Card 9 of 20
MediumStudy card 9
Prompt
How is \(x>416.67\) interpreted for a minimum whole count?
Move upward into the solution set.
Answer
The least feasible count is \(417\).
Example
Do not report \(416\).
Card 10 of 20
MediumStudy card 10
Prompt
How is \(x<11.67\) interpreted for a maximum whole count?
Move downward into the solution set.
Answer
The greatest feasible count is \(11\).
Example
Rounding to \(12\) violates the inequality.
Card 11 of 20
MediumStudy card 11
Prompt
Why is contextual integer selection not ordinary rounding?
Nearest is not the goal.
Answer
The chosen integer must satisfy the inequality and requested extreme.
Example
For \(n<9.8\), maximum whole \(n\) is \(9\).
Card 12 of 20
MediumStudy card 12
Prompt
How do you find when Company B is cheaper than Company A?
Preserve the requested direction.
Answer
Write the B expression less than the A expression and solve.
Example
Use \(B(x)<A(x)\).
Card 13 of 20
MediumStudy card 13
Prompt
Is a crossover point included in a strict cheaper-than result?
Move beyond equality.
Answer
No. At the crossover the prices are equal, not cheaper.
Example
If costs match at \(x=12\), strict savings begin on one side of \(12\).
Card 14 of 20
MediumStudy card 14
Prompt
What number-line endpoint represents an inclusive boundary?
Equality is allowed.
Answer
A closed endpoint.
Example
\(x\ge20\) is closed at \(20\).
Card 15 of 20
MediumStudy card 15
Prompt
What number-line endpoint represents a strict boundary?
Equality is excluded.
Answer
An open endpoint.
Example
\(x<50\) is open at \(50\).
Card 16 of 20
MediumStudy card 16
Prompt
What domain restriction commonly follows a contextual inequality?
Apply it after solving.
Answer
Counts may need to be nonnegative whole numbers.
Example
A package count cannot be \(-2\) or \(4.5\).
Card 17 of 20
MediumStudy card 17
Prompt
How should a proposed maximum count be checked?
Verify boundary behavior.
Answer
Test it in the original inequality and test the next integer to confirm it fails.
Example
If \(11\) works but \(12\) exceeds capacity, \(11\) is maximum.
Card 18 of 20
MediumStudy card 18
Prompt
What is a common pricing-comparison direction trap?
Translate ‘B costs less than A’ literally.
Answer
Writing the requested cheaper company on the greater-than side.
Example
Use \(B<A\), not \(A<B\).
Card 19 of 20
MediumStudy card 19
Prompt
What should a contextual inequality answer include?
Return from symbols to context.
Answer
The feasible range or requested extreme, with units and a contextual sentence.
Example
Say ‘at most \(14\) whole miles,’ not only \(x\le14\).
Card 20 of 20
HardStudy card 20
Prompt
How can a decreasing-resource inequality produce an upper time limit?
Track the negative coefficient.
Answer
Its negative rate causes sign reversal when time is isolated.
Example
From \(96-6h\ge30\), obtain \(h\le11\).
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