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Chapter 10: Problem 26

Determine each of the values. $$ -|-26| $$

Short Answer

Expert verified
The value is \(-26\).

Step by step solution

01

Simplify the Absolute Value

First, evaluate the absolute value inside the expression. The absolute value of a number is its distance from zero on the number line, without considering direction. Calculate \[|-26| = 26\]{}This is because the absolute value of \(-26\) is \(26\).
02

Apply the Negative Sign

Now, apply the negative sign outside of the absolute value that we simplified previously:\[\text{Evaluate } -|-26| = -26\]{}This is because the negative sign outside negates the positive value obtained from the absolute value.

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Key Concepts

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

Understanding Negative Numbers
Negative numbers are often confusing for many learners at first, but they follow simple rules once you get to know them. A negative number is any number less than zero. It is represented with a minus sign "-". Think of negative numbers as a way of saying that you owe something, or in temperature terms, when it's below freezing. Here are a Few Key Points:
  • Negative numbers are less than zero.
  • They're represented with a minus sign: -.
  • In practical terms, they often represent a lack, debt, or deficiency.

In the exercise, we started by considering the number \(-26\). The absolute value negates its negative status, but initially, it reminds us of its below-zero position on the number scale.
Visualizing with a Number Line
A number line is a visual representation of numbers placed sequentially along a straight line. It is particularly useful for understanding concepts like absolute value and negative numbers. On a basic number line:
  • Numbers to the right of zero are positive.
  • Numbers to the left of zero are negative.
  • Zero is the neutral point.

The absolute value of a number is its displacement from zero, regardless of the direction. When looking at \(-26\), it is 26 units to the left of zero. Therefore, its absolute value, \(|-26|\), equals 26 units because distance cannot be negative. Using a number line can help you easily see why the absolute value is positive.
Applying Mathematics Problem Solving
Mathematics problem solving involves breaking down problems into manageable steps. In the provided exercise, we used a structured approach:
  • Simplify the absolute value.
  • Apply any external operations, such as a negative sign.

For \-|-26|\, follow these steps:
  • First, evaluate the absolute value: \(|-26| = 26\).
  • Second, apply the negative sign: \(-26\).

By separating each operation, you isolate potential errors and improve understanding. This technique of step-by-step evaluation is useful for tackling various problems, ensuring you don't get overwhelmed as the calculations progress.

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Most popular questions from this chapter

Find the value of each of the following. Use a calculator to check each result. $$ -6+1-7 $$

Perform each operation. $$ -6+4 $$

Use the order of operations to simplify \(\left(5^{2}+3^{2}+2\right) \div 2^{2}\).

A number is positive if it is directly preceded by a __________ sign or no sign at all.

What numbers can replace \(x\) so that each statement is true? \(-3
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