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Chapter 1: Problem 88

Perform each indicated operation. $$ |-4-2|-|-8-1| $$

Short Answer

Expert verified
-3

Step by step solution

01

Evaluate the first absolute value expression

First, calculate the value inside the absolute value on the left: \(-4 - 2 = -6\). Now take the absolute value: \(|-6| = 6\).
02

Evaluate the second absolute value expression

Next, calculate the value inside the absolute value on the right: \(-8 - 1 = -9\). Now take the absolute value: \(|-9| = 9\).
03

Subtract the absolute values

Finally, subtract the two absolute values obtained in the previous steps: \(6 - 9 = -3\).

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Key Concepts

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

absolute value
Absolute value is a fundamental concept in mathematics, particularly in algebra. The absolute value of a number is its distance from zero on the number line, disregarding any negative sign. In essence, it turns any number into a non-negative number.
To express the absolute value, we use vertical bars, like this: \(|x|\).
For example:
  • \(|2| = 2\)
  • \(|-3| = 3\)
Absolute values are always non-negative and play a crucial role in many algebraic operations. In the given exercise, we evaluate the absolute values of \(-4 - 2\) and \(-8 - 1\) separately.
subtraction in algebra
Subtraction is one of the four basic arithmetic operations and involves taking one quantity away from another. In algebra, it is essential to follow the order of operations accurately. The operation follows the rule:
\text{Result} = \text{First Number} - \text{Second Number}
When dealing with negative numbers, it's crucial to pay attention to the signs. Negative signs can significantly affect the result.
For example:
  • \(-4 - 2 = -6\)
  • \(-8 - 1 = -9\)
In the example, we first deal with the expressions inside the absolute value bars by performing the subtraction.
negative numbers
Negative numbers are numbers less than zero, represented with a minus sign \((-\)). Understanding how to handle negative numbers is important in algebra. They often come up in subtraction and within absolute value operations.
When subtracting with negative numbers, follow these guidelines:
  • Subtracting a positive number from a negative number makes it more negative. E.g., \(-4 - 2 = -6\).
  • Subtracting a negative number from another negative number involves adding their absolute values together.
In the exercise, you handle the subtraction inside the absolute value first, resulting in negative outcomes. Once you have completed the subtraction, applying the absolute value converts the results into positive numbers before the final operation.

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Most popular questions from this chapter

Write each sentence as an equation, using \(x\) as the variable. Then find the solution of the equation from the set of integers between -12 and \(12,\) inclusive. An integer is divisible by 9 if the sum of its digits is divisible by \(9,\) and not otherwise. (a) Is 2,287,321 divisible by \(9 ?\) (b) Is 4,114,107 divisible by \(9 ?\)

Evaluate each expression for \(x=6, y=-4,\) and \(a=3\) \(\left(\frac{5}{6} x+\frac{3}{2} y\right)\left(-\frac{1}{3} a\right)\)

Solve each problem. The lowest temperature ever recorded in Illinois was \(-36^{\circ} \mathrm{F}\) on January \(5,1999 .\) The lowest temperature ever recorded in Utah was on February \(1,1985,\) and was \(33^{\circ} \mathrm{F}\) lower than Illinois's record low. What is the record low temperature for Utah? (Data from National Climatic Data Center.)

Use the distributive property to rewrite each expression. $$ -5.2(4 x+2.3) $$

Evaluate each expression for \(x=6, y=-4,\) and \(a=3\) \(5 x^{2}-4 y^{2}\)
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