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Questions and Answers
$30x ≤ 200$ represents the amount Ravi can spend on rice packets.
True
The sign '≥' means less than or equal to.
False
Reshma can spend up to 120 on registers and pens according to the inequality $40x + 20y ≤ 120$.
True
An equation must always involve the sign of inequality.
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Ravi’s equation $30x ≤ 200$ implies he can use all of his 200.
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Study Notes
Introduction to Linear Inequalities
- Linear inequalities contrast with equations as they include signs like '>', '≤', and '≥'.
- These inequalities represent conditions or limits rather than precise equalities.
- Useful applications span various fields including science, mathematics, statistics, economics, and psychology.
Understanding Inequalities through Examples
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Ravi's Rice Purchase:
- Has a budget of 200 to buy rice.
- Price per 1 kg packet of rice is 30.
- If x represents the number of packets purchased, the expenditure is given by the inequality 30x ≤ 200.
- Indicates Ravi cannot spend more than his budget, hence he might not buy the maximum possible.
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Reshma's Buying Scenario:
- Has 120 to spend on registers and pens.
- Each register costs 40 and each pen costs 20.
- Let x be the number of registers and y be the number of pens bought. The combined cost is represented by the inequality 40x + 20y ≤ 120.
- This inequality ensures her total expenditure does not exceed her available funds.
Key Concepts
- Linear inequalities are essential for translating real-world constraints into mathematical expressions.
- They provide a framework for making decisions based on limitations, such as budget or quantity restrictions.
- Understanding these inequalities is crucial for solving statement problems effectively.
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Description
This quiz covers the concepts of linear inequalities as introduced in Chapter 5 of your mathematics curriculum. You will explore how to translate statement problems into inequalities and understand their implications in various contexts. Sharpen your skills in solving and interpreting linear inequalities!
