Problem 57 In Exercises $1-66,$ compute t... [FREE SOLUTION]

91影视

Understanding Elementary Algebra with Geometry

Lewis Hirsch, Arthur Goodman

$Math Studyset 91影视 Explanations$ Math

6 Edition

Chapter 1: Problem 57

In Exercises $1-66,$ compute the value of each expression. $$-29+(-31)+51$$

Short Answer

Expert verified

The value of the expression is -9.

Step by step solution

- Combine Like Terms

First, notice that we have three terms: -29, -31 and 51. Beginning with the negative terms, combine -29 and -31.

- Add the Negative Numbers

Add the negative integers: -29 + (-31) = -29 - 31 = -60

- Add the Result to the Positive Term

Now add the result from Step 2 to the positive term, 51: -60 + 51 = -9

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Key Concepts

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

combining like terms

When working with algebraic expressions or just plain numbers, it's helpful to identify and group 'like terms'.
In simple terms, like terms are numbers or variables that have the same characteristics. For example, in the given exercise, the like terms are the negative numbers: -29 and -31.

By combining like terms, we simplify the calculation. In our case, we first add -29 and -31, because they are both negative integers.
This step makes operations easier and reduces the number of terms you have to deal with.
Always remember to first find and combine like terms to minimize mistakes.

negative numbers

Negative numbers can seem tricky at first, but they follow straightforward rules. A negative number is a number less than zero, often denoted with a minus sign (-).
For example, -29 is a negative number, just like -31.

One key rule for negative numbers is that when you add two negatives, you move further left on the number line.

So, -29 + (-31) becomes -29 - 31, which equals -60.

This rule helps you combine two negative numbers easily and correctly.
Always pay attention to the signs: adding two negatives increases the negativity, while adding a negative to a positive may decrease the overall value.

positive numbers

Positive numbers are numbers greater than zero. They are often what we think of when we count: 1, 2, 3, and so on.
In our example, 51 is a positive number.

Positive numbers have straightforward rules. Adding them means moving right on the number line.

When you combine positive and negative numbers, think of it as moving left (negative) and right (positive) on the number line.
In our exercise, after combining the negative numbers to get -60, we add the positive number 51, leading to -60 + 51.

Here, moving 51 steps right from -60 brings us to -9.
This is a useful way to visualize combining positive and negative terms.

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91影视

In Exercises \(1-66,\) compute the value of each expression. $$-29+(-31)+51$$

Short Answer

Step by step solution

- Combine Like Terms

- Add the Negative Numbers

- Add the Result to the Positive Term

Key Concepts

combining like terms

negative numbers

positive numbers

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