Ch. P - Fundamental Concepts of Algebra

Blitzer8th EditionCollege AlgebraISBN: 9780136970514Not the one you use?Change textbook

Blitzer 8th Edition

Ch. P - Fundamental Concepts of Algebra

Problem 104

Chapter 1, Problem 104

In Exercises 103–110, insert either <, >, or = in the shaded area to make a true statement. |−20| □ |−50|

Verified step by step guidance

Recall that the absolute value of a number is its distance from zero on the number line, always expressed as a non-negative value. So, for any number $a$, $|a| = \text{distance from zero}$.

Calculate the absolute value of the first number: $|-20|$. Since $-20$ is 20 units away from zero, $|-20| = 20$.

Calculate the absolute value of the second number: $|-50|$. Since $-50$ is 50 units away from zero, $|-50| = 50$.

Compare the two absolute values: $20$ and $50$. Determine which is greater, or if they are equal.

Based on the comparison, insert the correct symbol ($<$, $>$, or $=$) between $| -20 |$ and $| -50 |$ to make a true statement.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Absolute Value

The absolute value of a number is its distance from zero on the number line, always expressed as a non-negative value. For example, |−20| equals 20, and |−50| equals 50, regardless of the original sign.

Comparison of Numbers

Comparing numbers involves determining their relative size using symbols like <, >, or =. After evaluating absolute values, you compare the resulting positive numbers to decide which inequality symbol correctly represents their relationship.

Properties of Inequalities

Inequalities express the order between two values. Understanding that if one number is larger than another, the correct symbol is >, and if smaller, <, helps in correctly inserting the inequality symbol between expressions.

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