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Chapter 2: Problem 9

Determine whether inequality is true or false. \(0 \leq 8\)

Short Answer

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Step by step solution

01

Understand the Given Inequality

The inequality provided is: \(0 \leq 8\). This means we need to determine if 0 is less than or equal to 8.
02

Compare the Numbers

Compare the numbers directly. In this case, 0 is indeed less than 8.
03

Verify the Inequality

Since 0 is less than 8, 0 is also less than or equal to 8. Therefore, the inequality \(0 \leq 8\) is true.

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Key Concepts

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

inequality comparison
When solving inequalities, it's essential to understand what an inequality symbol means. The inequality symbol \( \leq \) stands for 'less than or equal to.' This tells us there are two possible scenarios: either the number on the left is less than the number on the right or both numbers are equal.

In our example, the inequality is \(0 \leq 8 \). This means we need to check if 0 is less than or exactly equal to 8.

By directly comparing these two numbers, we can see that 0 is less than 8. Since one of the conditions (0 being less than 8) is met, the inequality is true.

Remember:
  • The \( \gt \) symbol means 'greater than.'
  • The \( \geq \) symbol means 'greater than or equal to.'
  • The \( < \) symbol means 'less than.'
Understanding these symbols is key to correctly interpreting and solving inequalities.
number relationships
Understanding number relationships helps us see how numbers compare on the number line.

When we look at 0 and 8, we can visualize a number line to confirm their relationship.

Zero starts at a point on the left side, and as we move to the right, we get larger numbers. Since 8 is to the right of 0 on the number line, it tells us that 0 is less than 8. Because of this, we can comfortably say that \(0 \leq 8 \) is true.

Knowing how to locate numbers on a number line can make solving inequalities simpler.
  • Numbers to the left are always smaller than numbers to the right.
  • If two numbers are the same, their inequality comparison will be equal.
Practice with visual aids like number lines can help strengthen your understanding of these relationships.
mathematical reasoning
Mathematical reasoning involves using logic to solve problems. When working with inequalities, it鈥檚 not just about comparing numbers; it's about understanding why they relate in a certain way.

In our example, we used reasoning to determine the truth of \(0 \leq 8 \).

We started by understanding what \( \leq \) means: less than or equal to.

Next, we compared 0 and 8 to confirm that 0 is indeed less than 8.

These steps show the logic behind our solution, making not just a correct guess but a thoughtful conclusion.

Effective reasoning includes:
  • Breaking down the inequality into parts.
  • Understanding each part's meaning.
  • Applying logical steps to arrive at an answer.
Using reasoning skills improves your ability to tackle various mathematical problems reliably.

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Most popular questions from this chapter

Show a complete solution to each problem. Chance meeting. In 6 years Todd will be twice as old as Darla was when they met 6 years ago. If their ages total 78 years, then how old are they now?

Solve each problem. The area of a triangle is 40 square meters. If the height is 10 meters, then what is the length of the base?

Solve each inequality. Write the solution set using interval notation. $$1<|x+2|$$

Show a complete solution to each problem. Rectangular room. If the perimeter of a rectangular room is \(38 \mathrm{m}\) and the length is \(1 \mathrm{m}\) longer than twice the width, then what are the length and width?

Exploration a) Evaluate \(|m+n|\) and \(|m|+|n|\) for i) \(m=3\) and \(n=5\) ii) \(m=-3\) and \(n=5\) iii) \(m=3\) and \(n=-5\) iv) \(m=-3\) and \(n=-5\) b) What can you conclude about the relationship between \(|m+n|\) and \(|m|+|n| ?\)
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