/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 16 Evaluate each expression if \(a=... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 16

Evaluate each expression if \(a=-5, b=6,\) and \(c=2.8\). \(|-4 b|\)

Short Answer

Expert verified
24

Step by step solution

01

Substitute Values

Substitute the value of \( b=6 \) into the expression \( |-4b| \). This gives us \( |-4 \times 6| \).
02

Calculate the Multiplication

Multiply \(-4\) by \(6\). This results in \(-24\). So, the expression becomes \(|-24|\).
03

Apply the Absolute Value

Apply the absolute value function to \(-24\). The absolute value of a number is the distance of the number from zero on the number line, disregarding any negative sign. Thus, \(|-24| = 24\).

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

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

Substitution
Substitution is a technique used in mathematics where a variable in an expression is replaced with its given value. This process helps in simplifying expressions, especially when specific values are given for the variables. In our exercise, we are asked to evaluate the expression \(|-4b|\) with a specified value for \(b\). Here, \(b\) is given as \(6\). To substitute means to replace \(b\) in the expression with \(6\). Thus, the expression \(|-4b|\) becomes \(|-4 \times 6|\) after substitution. This step is crucial because it turns a general expression into a numeric one that can be further simplified or directly calculated.
Multiplication
Multiplication is a fundamental arithmetic operation where one number is combined with itself a specific number of times, represented as factors. It鈥檚 important to understand, especially when dealing with expressions that include several terms multiplied together. In the exercise, after substituting \(b\) with \(6\), we need to calculate the result of \(-4 \times 6\). Here's a friendly reminder of how multiplication works with negative numbers:
  • When multiplying a positive and a negative number, the result is negative.
  • Multiply the absolute values of the numbers to get the magnitude.
So, \(-4 \times 6 = -24\). Now, the expression becomes \(|-24|\), ready for further evaluation.
Distance on Number Line
The distance on a number line is interpreted as the absolute value in mathematics. The absolute value of a number refers to how far that number is from zero, without considering the direction.In the context of our problem, after computing the multiplication, we got \-24\. This number鈥檚 position or distance from zero is key in understanding absolute value. For \-24\, the absolute value \(|-24|\) simply becomes \24\ because absolute value removes any negative sign:
  • No matter where you are on the number line, absolute value always brings you back to zero, ignoring the negative.
  • It transforms negative distances into positive ones because we鈥檙e only interested in the size of the step, not the direction.
Thus, the absolute value application results in \24\, which is the final step and solution of the expression evaluation.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Evaluate each expression if \(a=3, b=-2,\) and \(c=1.2 .(\text { lesson } 1-1)\) \(c^{2}-a b\)

Simplify each expression. $$ 6 a-2 b-3 a+9 b $$

Define a variable and write an inequality for each problem. Then solve. The difference of one half of a number and 7 is greater than or equal to 5

Solve each inequality. Graph the solution set on a number line. $$ |g+4| \leq 9 $$

PREREQUISITE SKILL Identify the additive inverse for each number or expression. 25
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Probability and Statistics

Read Explanation

Logic and Functions

Read Explanation

Statistics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Mechanics Maths

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.