/*! 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 54 Evaluate each expression. $$|1... [FREE SOLUTION] | 91影视

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Chapter 1: Problem 54

Evaluate each expression. $$|15|-|7+3|$$

Short Answer

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5

Step by step solution

01

Apply the Absolute Value

First, calculate the absolute value of the number 15. The absolute value of any number is its distance from zero, without considering the direction (positive or negative). We have |15| = 15.
02

Evaluate the Expression Inside the Other Absolute Value

Next, evaluate the expression inside the second absolute value. We need to calculate |7 + 3|. Add 7 and 3 to get 10. Therefore, we have |7 + 3| = |10|.
03

Apply the Absolute Value Again

Now, calculate the absolute value of 10. Since the absolute value of any positive number is the number itself, we have |10| = 10.
04

Subtract the Values

Finally, subtract the second absolute value from the first absolute value as follows: 15 - 10 = 5.

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Key Concepts

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

Evaluate Expressions
Evaluating expressions involves finding the value of an expression by performing arithmetic operations and following the order of operations. In our example expression \( |15| - |7+3| \), we need to break it down step by step. First, we apply the absolute value to 15, which remains 15 because it's already positive. Next, we simplify the expression inside the absolute value by adding 7 and 3 to get 10. Finally, we apply the absolute value to 10 and subtract it from 15.
Absolute Value Operations
Absolute value is a core mathematical concept that represents the distance of any number from zero on the number line. The absolute value of any number is always non-negative. For positive numbers, it's the number itself, and for negative numbers, it's the positive version of that number.
Let's break down the rules:
  • The absolute value of a positive number (like 15) is the number itself: \( |15| = 15 \).
  • The absolute value of 0 is 0: \( |0| = 0 \).
  • The absolute value of a negative number (like -10) is the positive counterpart of that number: \( |-10| = 10 \).
In our exercise, we first determined that \(|15| = 15\) and then simplified \(|7 + 3| = |10| = 10\).
Basic Arithmetic
Basic arithmetic encompasses the fundamental operations of addition, subtraction, multiplication, and division that we use to manipulate numbers. Understanding and mastering basic arithmetic is critical because it's the foundation of more complex mathematical concepts.
In our example:
  • We performed an addition: 7 + 3 = 10.
  • Then, we applied absolute values.
  • Finally, we subtracted the second absolute value from the first: 15 - 10 = 5.
These steps show how essential basic arithmetic is in evaluating and simplifying expressions.

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Most popular questions from this chapter

At the beginning of the month Carla's checking account had a balance of \(\$ 643.47,\) while at the end of the month the balance was \(-\$ 82.94 .\) If she made no deposits during this month, what was the total of the checks that Carla wrote during this month?

Locate the given number between two successive integers on the number line. For example, if the given number is \(2.6,\) it is located between 2 and 3 on the number line. $$0.24$$

Compute the given expression. Round off your answer to two decimal places where necessary. $$\frac{-8.4}{1.2}$$

In Exercises \(73-84\), evaluate the given expression. $$9-5 \cdot 4-2$$

Factor the given number into its prime factors. If the number is prime, say so. $$3,024$$
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