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Chapter 2: Problem 70

OPEN ENDED Write two inequalities using integers

Short Answer

Expert verified
First inequality: \(3 < 7\). Second inequality: \(7 > 3\).

Step by step solution

01

Define the Integers for the Inequalities

Choose two integers. For this problem, let's select 3 and 7.
02

Formulate the First Inequality

Using the integers chosen, write an inequality. For this example, one possible inequality is \( 3 < 7 \). This inequality shows that 3 is less than 7.
03

Formulate the Second Inequality

Write a different inequality involving integers. We can use the integers 3 and 7 again but flip their positions to write \( 7 > 3 \). This inequality also shows the relationship between the two numbers, but in reverse order.

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Key Concepts

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

Integers
Integers are a fundamental concept in mathematics. They encompass whole numbers and their negative counterparts, excluding fractions and decimals. Key points about integers:
  • They are denoted by the symbol \( \mathbb{Z} \).
  • Include numbers like -3, 0, 4, etc.
  • Used in counting, ordering, and simple arithmetic.
Integers are crucial in forming inequalities, showing the relative size or order of numbers. For example, when you have two integers like 3 and 7, you can establish a relation between them using the signs \(<\) and \(>\), signifying 'less than' and 'greater than', respectively.
Math Problem-Solving
Math problem-solving involves breaking down problems into manageable steps and using logic to find a solution. When dealing with mathematical inequalities, it begins with understanding the problem, followed by selecting integers that clearly demonstrate the relationship being expressed.Steps to solve math problems involving inequalities:
  • Identify and define the numbers involved.
  • Determine the inequality's direction based on these numbers.
  • Write the inequality clearly, for instance, \( 3 < 7 \).
  • Verify the inequality by considering the positions of numbers on a number line.
Successful problem-solving in math often involves double-checking your work to ensure accuracy, particularly when dealing with inequalities where the order matters.
Prealgebra
Prealgebra is the stage in mathematics where you begin to explore fundamental algebraic concepts using basic arithmetic. It introduces students to expressions, simple equations, and inequalities. This forms the foundation for algebraic thinking and problem-solving.Key components of prealgebra include:
  • Understanding and manipulating numbers and operations.
  • Learning about variables and their usage.
  • Recognizing patterns and relationships between numbers.
  • Working with inequalities to compare integers.
In the context of inequalities, prealgebra teaches students how to recognize the relationship between two numbers and represent it using symbols like \(<\) and \(>\). For instance, by choosing integers 3 and 7, a prealgebra student learns to express both \(3 < 7\) and its reverse, \(7 > 3\), understanding the inherent logic and ordering of numbers.

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