Ch. R - Review of Basic Concepts

Lial13th EditionCollege AlgebraISBN: 9780136881063Not the one you use?Change textbook

Lial 13th Edition

Ch. R - Review of Basic Concepts

Problem 19

Chapter 1, Problem 19

Determine whether each statement is true or false. |5+(-13) | = |5| + |-13|

Verified step by step guidance

Recall the definition of absolute value: for any real number $a$, $|a|$ represents the distance of $a$ from zero on the number line, and it is always non-negative.

Evaluate the left side of the equation: calculate $|5 + (-13)|$. First, perform the addition inside the absolute value: $5 + (-13) = 5 - 13$.

Simplify the sum inside the absolute value: $5 - 13 = -8$, so the left side becomes $|-8|$.

Evaluate the right side of the equation: calculate $|5| + |-13|$. Find the absolute values separately: $|5|$ and $|-13|$.

Compare the two sides: check if $|-8|$ is equal to $|5| + |-13|$. Since $|-8| = 8$, $|5| = 5$, and $|-13| = 13$, determine if $8 = 5 + 13$.

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 Definition

The absolute value of a number is its distance from zero on the number line, always expressed as a non-negative value. For example, |5| = 5 and |-13| = 13, regardless of the sign of the original number.

Properties of Absolute Value

Absolute value has specific properties, such as |a| ≥ 0 and |a| = |-a|. Importantly, the absolute value of a sum is not generally equal to the sum of the absolute values, i.e., |a + b| ≠ |a| + |b| in most cases.

Evaluating Expressions with Absolute Values

To evaluate expressions involving absolute values, first simplify inside the absolute value, then apply the absolute value operation. For example, |5 + (-13)| = |-8| = 8, while |5| + |-13| = 5 + 13 = 18, showing the two sides can differ.

Recommended video:

Guided course

03:11

Evaluating Algebraic Expressions

Related Practice

Textbook Question

Use set notation, and list all the elements of each set. {12, 13, 14,..., 20}

views

Textbook Question

Write each improper fraction as a mixed number. 77/12

views

Textbook Question

Find the domain of each rational expression. x³ - 1 / x - 1

views

Textbook Question

Identify each expression as a polynomial or not a polynomial. For each polynomial, give the degree and identify it as a monomial, binomial, trinomial, or none of these. (3/8)x⁵-(1/x²)+9

views

Textbook Question

Factor out the greatest common factor from each polynomial. See Example 1. $4 k^{2} m^{3} + 8 k^{4} m^{3} - 12 k^{2} m^{4}$

Textbook Question

Determine whether each statement is true or false. |8-12| = |8| - |12|

views