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Chapter 2: Problem 7

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

Short Answer

Expert verified
\(b < a\)

Step by step solution

01

- Identify the Given Relationship

The sentence given is: 'b is less than a'. This implies a relationship where b is smaller than a.
02

- Translate the Sentence to a Mathematical Inequality

The phrase 'b is less than a' can be directly translated into the inequality: \(b < a\).
03

- Match with the Given Inequalities

Now, compare the inequality \(b < a\) with the provided options: 1. \(a < b \)2. \(a \leq b \)3. \(b < a \)4. \(b \leq a \)The correct match is: \(b < a\).

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Key Concepts

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

inequality notation
Inequality notation is used to compare two values. It tells us whether one value is larger or smaller than the other. There are four main symbols in inequality notation:
  • '<' means less than.
  • '>' means greater than.
  • '鈮�' means less than or equal to.
  • '鈮�' means greater than or equal to.
Inequalities allow us to express relationships that are not equal, such as '3 < 5' or '7 鈮� 3'.
translating sentences to inequalities
Translating sentences into inequalities involves converting words into mathematical symbols. For example, the sentence: 'b is less than a' can be translated step by step:
  • Identify the values to compare: 'b' and 'a'.
  • Determine the relationship: 'less than'.
  • Use the appropriate symbol: '<'.
So, 'b is less than a' becomes:
\( b < a \).
Similarly, 'a is greater than or equal to b' is translated to: \( a \geq b \).
comparison of inequalities
Comparing inequalities involves looking at the mathematical symbols and relationships to determine how values relate to one another. For instance:
  • 'b < a': 'b' is strictly less than 'a'.
  • 'a 鈮� b': 'a' is less than or equal to 'b'.
  • 'b 鈮� a': 'b' is greater than or equal to 'a'.
  • 'a > b': 'a' is strictly greater than 'b'.
By comparing these inequalities, one can understand their relative positions and the specific conditions each statement implies.

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Most popular questions from this chapter

Use an inequality and the five-step process to solve each problem. Abriana rented a compact car for a business trip. At the time of the rental, she was given the option of prepaying for an entire tank of gasoline at \(\$ 3.099\) per gallon, or waiting until her return and paying \(\$ 6.34\) per gallon for enough gasoline to fill the tank. If the tank holds 14 gal, how many gallons can she use and still save money by choosing the second option?

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.

Review operations with real numbers. Simplify. $$ -6.3+(-4.8) $$

Annette claims the following problem has no solution: "The sum of the page numbers on facing pages is \(191 .\) Find the page numbers." Is she correct? Why or why not?

Translate to an inequality. The time of the test was between 45 min and 55 min.
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