Table of contents

0. Review of Algebra4h 18m
1. Equations & Inequalities3h 18m
2. Graphs of Equations43m
3. Functions2h 17m
4. Polynomial Functions1h 44m
5. Rational Functions1h 23m
6. Exponential & Logarithmic Functions2h 28m
7. Systems of Equations & Matrices4h 6m
8. Conic Sections2h 23m
9. Sequences, Series, & Induction1h 22m
10. Combinatorics & Probability1h 45m

0. Review of Algebra

Exponents

College Algebra

0. Review of Algebra

Exponents

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2:09 minutes

Problem 39

Textbook Question

Find each sum or difference. -6 - 5

Verified step by step guidance

Identify the operation: This problem involves subtraction, specifically finding the difference between two numbers.

Rewrite the expression: The expression is \(-6 - 5\).

Consider the operation: Subtracting a positive number is the same as adding its negative. So, \(-6 - 5\) can be rewritten as \(-6 + (-5)\).

Combine the numbers: When adding two negative numbers, you add their absolute values and keep the negative sign.

Calculate the sum of the absolute values: Add \(6\) and \(5\) to find the result, and then apply the negative sign to the sum.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Integer Operations

Integer operations involve the basic arithmetic functions of addition and subtraction applied to whole numbers, both positive and negative. Understanding how to manipulate integers is crucial, as it lays the foundation for more complex mathematical concepts. For example, subtracting a positive integer from a negative integer results in a more negative value.

Subtraction as Addition of Opposites

Subtraction can be understood as the addition of the opposite value. This means that when you subtract a number, you can instead add its negative. For instance, the expression -6 - 5 can be rewritten as -6 + (-5), which simplifies the process of finding the result by focusing on addition.

Number Line Visualization

Using a number line is a helpful visual tool for understanding operations with integers. It allows students to see the relative positions of numbers and how they change with addition or subtraction. For example, starting at -6 and moving 5 units to the left on the number line illustrates the result of the operation clearly.