Problem 36 In Exercises $1-66,$ compute t... [FREE SOLUTION]

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Understanding Elementary Algebra with Geometry

Lewis Hirsch, Arthur Goodman

$Math Studyset 91影视 Explanations$ Math

6 Edition

Chapter 1: Problem 36

In Exercises $1-66,$ compute the value of each expression. $$-10+6+(-1)$$

Short Answer

Expert verified

-5

Step by step solution

- Identify the terms

The expression given is \[ -10 + 6 + (-1) \]. The terms to evaluate are -10, +6 and -1.

- Combine the first two terms

Start by adding -10 and +6: \[ -10 + 6 = -4 \].

- Combine the result with the next term

Next, add -4 and -1: \[ -4 + (-1) = -5 \].

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Key Concepts

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

Order of Operations

When dealing with mathematical expressions, it's essential to follow the proper order of operations to get the correct result. The order of operations dictates the sequence in which you should carry out different mathematical actions. For instance:

Parentheses: Always start with operations inside parentheses.
Exponents: Solve any exponents next.
Multiplication and Division: Work these from left to right.
Addition and Subtraction: Finally, handle these from left to right.

In our example, -10 + 6 + (-1) , the term order doesn't change the addition process, but maintaining consistency is critical. By always following the prescribed order, mistakes are minimized.

Integer Addition

Integer addition is a fundamental concept in algebra. It deals with adding both positive and negative numbers:

Positive numbers are added as usual.
Negative numbers require you to imagine them on a number line, moving left for subtraction.
Adding a positive and a negative number reduces the result by the value of the smaller one.

In the expression -10 + 6 + (-1) , we start with -10 and add 6 which moves us to -4 (since -10 + 6 = -4 ). Then, adding -1 to -4 pushes the value back to -5 ( -4 + (-1) = -5 ).

Step-by-Step Algebra

Breaking down problems into smaller, manageable steps is known as Step-by-Step Algebra. This method helps to avoid mistakes and ensures clarity:

First, identify the terms to be combined.
Next, perform the calculations gradually.
Ensure each step is verified before moving to the next.

Using our example:

Identify terms: -10, +6, -1
Combine first two terms: -10 + 6 = -4
Combine the result with the next term: -4 + (-1) = -5

By following each step methodically, you minimize errors and develop a clearer understanding of the process.

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91影视

In Exercises \(1-66,\) compute the value of each expression. $$-10+6+(-1)$$

Short Answer

Step by step solution

- Identify the terms

- Combine the first two terms

- Combine the result with the next term

Key Concepts

Order of Operations

Integer Addition

Step-by-Step Algebra

One App. One Place for Learning.

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