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Chapter 2: Problem 6

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

Short Answer

Expert verified
b \leq a

Step by step solution

01

Understand the Statement

The statement given is 'b is no less than a.' This means that b is either greater than or equal to a.
02

Identify the Inequality

If 'b is no less than a,' this means two possibilities: b could be greater than a, or b could be equal to a. This translates to b being either greater than or equal to a.
03

Match with Given Inequalities

The inequality that matches the statement 'b is no less than a' is the one that states b is greater than or equal to a. Among the given options, the correct inequality is: \( b \leq a \).

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Key Concepts

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

Inequality Symbols
Inequality symbols are used to show that one value is different from another. They can signify that one value is larger, smaller, or equal to another. The following are the most common inequality symbols:
  • Less than: \(a < b\)
  • Greater than: \(a > b\)
  • Less than or equal to: \(a \leq b\)
  • Greater than or equal to: \(a \geq b\)
These symbols are essential in comparing two values and are fundamental in algebra and calculus. It's important to differentiate between them to accurately solve and interpret mathematical expressions.
Algebraic Expressions
Algebraic expressions are combinations of numbers, variables, and arithmetic operations. For example, \(3x + 2\), \(a - b\), and \(5y\) are all algebraic expressions. In the context of inequalities, algebraic expressions often represent the quantities being compared. Understanding how to manipulate and interpret these expressions is crucial.

In the given exercise, '\(b\) is no less than \(a\)' translates into an algebraic inequality where you need to express the relationship between \(a\) and \(b\). Recognizing that 'no less than' means 'greater than or equal to' helps in forming the correct inequality, \(b \geq a\).
Comparative Statements
Comparative statements are sentences that compare two values or expressions. They use terms like 'greater than', 'less than', or 'equal to'. For example, '5 is greater than 3' or 'x is less than or equal to y'. These statements are translated into mathematical notation using inequality symbols.

In the given problem, the statement 'b is no less than a' is a comparative statement. To solve it, you need to understand that 'no less than' indicates either an equal or a greater value. Therefore, you match it with the inequality symbol that represents this relationship, which is \(b \geq a\).

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Most popular questions from this chapter

The second side of a triangle is \(3.25 \mathrm{cm}\) longer than the first side. The third side is \(4.35 \mathrm{cm}\) longer than the second side. If the perimeter of the triangle is 26.87 \(\mathrm{cm},\) find the length of each side.

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

Use an inequality and the five-step process to solve each problem. The formula \(R=-0.0065 t+4.3259\) can be used to predict the world record, in minutes, for the 1 -mi run \(t\) years after \(1900 .\) Determine (in terms of an inequality) those years for which the world record will be less than \(3.6 \mathrm{min}\)

Abraham Lincoln's 1863 Gettysburg Address refers to the year 1776 as "four score and seven years ago." Determine what a score is.

The perimeter of a rectangle is \(101.74 \mathrm{cm} .\) If the length is \(4.25 \mathrm{cm}\) longer than the width, find the dimensions of the rectangle.
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