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Chapter 2: Problem 4

Match the sentence with one of the following: $$ a

Short Answer

Expert verified
\( a < b \)

Step by step solution

01

Understand the given phrase

The phrase 'a is exceeded by b' means that the value of \(a\) is less than the value of \(b\).
02

Compare the phrase to given inequalities

We need to match 'a is exceeded by b' with one of the given inequalities: \( a < b \); \( a \leq b \); \( b < a \); \( b \leq a \).
03

Determine the correct inequality

The correct inequality that represents 'a is exceeded by b' is \( a < b \), which reads as 'a is less than b'.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

inequalities
Inequalities are a fundamental concept in algebra, used to compare the relative sizes of two values. Unlike equations that show equality, inequalities show a comparative relationship where one value is greater than, less than, or sometimes equal to another. The symbols used to represent inequalities include: `<`, `>`, `鈮, and `鈮, meaning less than, greater than, less than or equal to, and greater than or equal to, respectively. In the provided exercise, the focus is on understanding phrases like 'a is exceeded by b' and turning these phrases into an algebraic inequality, which in this case is expressed as 'a < b'.
algebraic expressions
Algebraic expressions are combinations of variables, numbers, and at least one arithmetic operation (such as addition or multiplication) without an equality sign. They are the building blocks of algebraic equations and inequalities. In this exercise, the expressions involved are simple: just two variables, `a` and `b`, and the comparison between them using inequality signs. When forming an algebraic inequality, it is important to clearly understand how the variables are related as described in statements or word problems. For instance, 'a is exceeded by b' translates to the algebraic expression `a < b`.
comparative relations
Comparative relations in algebra help describe how one quantity relates to another. They are often used to formulate and solve real-world problems. By understanding these relations through inequalities, we can better comprehend how different values compare. For instance, 'a is exceeded by b' means that the value of `a` is less than `b`, thus forming the inequality `a < b`. Recognizing and correctly interpreting comparative phrases allows one to set up accurate inequalities which are essential in further mathematical problem solving.

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Most popular questions from this chapter

Match the sentence with one of the following: $$ a

Use an inequality and the five-step process to solve each problem. Rick's Automotive charges \(\$ 50\) plus \(\$ 15\) for each \((15-\text { min })\) unit of time when making a road call. Twin City Repair charges \(\$ 70\) plus \(\$ 10\) for each unit of time. Under what circumstances would it be more economical for a motorist to call Rick's?

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Match the sentence with one of the following: $$ a
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