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.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.

Video duration:

Was this helpful?

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.

Recommended video:

06:07

Linear Inequalities

Related Practice

Textbook Question

Factor completely, or state that the polynomial is prime. 3x^4-12x^2

326

views

Textbook Question

In Exercises 103–114, factor completely. 6x⁴+35x²−6

964

views

Textbook Question

Factor and simplify each algebraic expression. $16 x^{- \frac{3}{4}} + 32 x^{\frac{1}{4}}$

Simplify by reducing the index of the radical. $the fourth root of 7 squared$

811

views

Textbook Question

Perform the indicated computations. Write the answers in scientific notation. If necessary, round the decimal factor in your scientific notation answer to two decimal places. 282,000,000,000/0.00141

1056

views

Textbook Question

Factor and simplify each algebraic expression. $-8(4x + 3)^{-2} + 10(5x + 1)(4x + 3)^{-1}$

868

views