Problem 95 Write a true sentence using eith... [FREE SOLUTION]

Chapter 1: Problem 95

Write a true sentence using either $<,>,$ or $=$. $$|23| \square|-23|$$

Short Answer

Expert verified

$|23| = |-23|$

Step by step solution

Understand the Absolute Value

The absolute value of a number is its distance from zero on the number line, regardless of direction. Therefore, both $|23|$ and $-23|$ will yield positive values.

Calculate the Absolute Values

Calculate the absolute value of 23: $|23| = 23$. Calculate the absolute value of -23: $|-23| = 23$.

Compare the Values

Both absolute values calculated are 23. Therefore, $|23| = | -23|$.

Write the True Sentence

Substitute the values into the original expression to get: $|23| = | -23|$.

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Key Concepts

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

Understanding Algebra

Algebra is a branch of mathematics that deals with symbols and the rules for manipulating those symbols. It's a step forward from arithmetic. While arithmetic uses numbers to perform basic operations like addition and subtraction, algebra uses variables (like x or y) to represent numbers and express relationships between them.

This problem involving absolute values is an example of how algebra can help you compare different entities. As you work through algebraic problems, you often need to solve equations, simplify expressions, or understand relationships involving variables.

Grasping Inequalities

Inequalities are mathematical statements used to compare two values. They tell us whether one value is larger, smaller, or equal to another. You'll typically see symbols like <, >, 鈮�, and 鈮� in these comparisons.

In the given problem, you are asked to use the appropriate comparison operator (either <, >, or =) to state the relationship of the absolute values of 23 and -23. Since absolute values measure the distance from zero without considering direction, $ |23| = 23 $ and $ | -23| = 23 $. Therefore, the correct inequality symbol here is =. Inequalities are essential in expressing limits, ranges, and conditions in algebra.

Visualizing with a Number Line

A number line is a straight line with numbers placed at equal intervals along its length. It's a useful tool for visualizing numbers, their order, and even their absolute values.

In the context of absolute values, you can see that both 23 and -23 have the same distance from zero. Whether you move 23 units to the right or 23 units to the left of 0, the distance remains the same. This visualization can help make sense of why $|23| = |-23|$.

Number lines can also aid in understanding other concepts in algebra and inequalities, such as plotting points, visualizing the solutions of equations, and demonstrating inequality regions.

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91影视

Write a true sentence using either \(<,>,\) or \(=\). $$|23| \square|-23|$$

Short Answer

Step by step solution

Understand the Absolute Value

Calculate the Absolute Values

Compare the Values

Write the True Sentence

Key Concepts

Understanding Algebra

Grasping Inequalities

Visualizing with a Number Line

One App. One Place for Learning.

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