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Chapter 1: Problem 122

Simplify. $$ \operatorname{abs}(-7) $$

Short Answer

Expert verified
The absolute value of -7 is 7.

Step by step solution

01

Identify the Absolute Value Function

The problem requires us to find the absolute value of -7, denoted as \( \operatorname{abs}(-7) \). The absolute value of a number is its distance from zero on a number line, without considering its direction (positive or negative).
02

Apply the Absolute Value Property

The absolute value of a negative number is obtained by removing its negative sign. Therefore, \( \operatorname{abs}(-7) = 7 \).

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Key Concepts

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

Negative Numbers
Negative numbers are numbers with a value less than zero. They often have a minus sign (-) in front of them to indicate their value is below zero. For example, in the integer -7, the number 7 is made negative by the minus sign.
Negative numbers are useful in various real-life situations, such as representing debts in finance or temperatures below freezing.
Understanding negative numbers is crucial, and one thing to always remember is:
  • Adding a negative number is like subtracting its positive form.
  • Multiplying two negative numbers results in a positive number.
  • Dividing two negative numbers also leads to a positive number.
Mastering the concept of negative numbers and their properties is essential for solving many mathematical problems.
Number Line
A number line is a straight, horizontal line that graphically represents numbers as points at consistent distances along the line. It's a central tool in mathematics for understanding how numbers relate to each other.
Each point on a number line corresponds to a number, and the position indicates its value.
  • Zero is typically at the center of the number line.
  • Positive numbers lie to the right of zero.
  • Negative numbers lie to the left of zero.
When we talk about the absolute value, the number line is invaluable because it helps show the distance a number is from zero, ignoring any direction. Thus, both -7 and 7 are 7 units away from zero, showcasing their absolute value as precisely 7.
Simplifying Expressions
Simplifying expressions involves reducing them to their most basic form without changing their value. In the context of absolute values, simplifying means finding the distance of a number on the number line from zero.
Here's a quick guide on simplifying absolute value expressions:
  • If the number is positive or zero, its absolute value is the number itself.
  • If the number is negative, remove the negative sign to get its absolute value.
Let's consider the expression \( \operatorname{abs}(-7) \). Since -7 is negative, we remove the negative sign to get 7.
Simplifying expressions is a key part of solving algebraic equations and helps in making complex problems much more manageable.

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