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 22

Chapter 1, Problem 22

Determine whether each statement is true or false. |-5| ∙ |6| = |-5∙6|

Verified step by step guidance

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

Calculate the left side of the equation: $|-5| * |6|$. Since $|-5| = 5$ and $|6| = 6$, multiply these two values to get $5 * 6$.

Calculate the right side of the equation: $|-5 * 6|$. First, multiply $-5$ and $6$ to get $-30$, then find the absolute value $|-30|$.

Compare the results from the left side and the right side to see if they are equal.

Conclude whether the statement $|-5| * |6| = |-5*6|$ is true or false based on the comparison.

Verified video answer for a similar problem:

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

Video duration:

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, |-5| equals 5, and |6| equals 6, regardless of the original sign of the number.

Properties of Absolute Value

One key property is that the absolute value of a product equals the product of the absolute values: |a * b| = |a| * |b|. This means multiplying inside the absolute value or multiplying the absolute values separately yields the same result.

Evaluating Expressions with Absolute Values

To evaluate expressions like |-5| * |6| and |-5*6|, compute each absolute value first, then perform multiplication. This step-by-step approach helps verify if the equality holds true by comparing both sides.

Recommended video:

03:11

Evaluating Algebraic Expressions

Related Practice

Textbook Question

Simplify each expression. $(35m^4n)$\left$(-$\frac{2}{7}$mn^2$\right$)$

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. 9

Textbook Question

Determine whether each statement is true or false. |11| * |-6| = |-66|

views

Textbook Question

Factor out the greatest common factor from each polynomial. See Example 1. 6x(a+b)-4y(a+b)

views

Textbook Question

Write each mixed number as an improper fraction. $2 and three fifths$

views

Textbook Question

Write each rational expression in lowest terms. 8x² + 16 / 4x²