Problem 10 - Elementary Algebra

Question

Simplify. (Assume all denominators are nonzero.) $$ 2-121+34 $$

Step-by-Step Solution

Answer

The simplified result is -85.

Step 1: Identify Components

First, identify the numbers involved in the expression. This expression consists of 2, -121, and 34.

Step 2: Compute the Addition of Positive Numbers

Add the positive numbers together. In this expression, that would be \(2 + 34 = 36\).

Step 3: Perform Subtraction

Now, subtract the larger negative number from the result of Step 2. Calculate \(36 - 121\), which is equal to \(-85\).

Key Concepts

Understanding Integer Operations

Integer operations are the basic building blocks of algebra. When you perform operations like addition or subtraction with integers, you are engaging in integer operations. Integers include whole numbers, both positive and negative, and zero. No fractions or decimals fall into this category.

• Example of integers: -3, 0, 4.
• They can be added, subtracted, multiplied, or divided.
• In our exercise: 2, -121, and 34 are integers.

To simplify an expression involving integer operations, you often need to focus on one type of operation at a time. This means handling all additions first, before moving onto subtractions. Doing so makes the process more manageable and reduces the chances of making mistakes.
Let's simplify the expression step-by-step as was presented; start by organizing the numbers based on their positive and negative nature.

Addition and Subtraction with Integers

Addition and subtraction of integers require an understanding of how positive and negative numbers interact with each other. When you add or subtract these integers, there are some straightforward rules.

• Adding two positive integers results in a positive integer.
• Adding two negative integers results in a negative integer.
• Subtracting a negative is the same as adding a positive.
• Subtracting a positive is the same as adding a negative.

In our original problem, we first add the positive numbers: 2 and 34. Adding these gives us 36.
Next, we handle subtraction. To simplify the expression, we subtract 121 from 36. This involves dealing with both positive and negative numbers together. The key is to keep track of signs and perform operations step-by-step.

Working with Positive and Negative Numbers

Positive and negative numbers can sometimes be tricky, especially when working with both in the same problem. However, some fundamental concepts make it manageable:

• Positive numbers are greater than zero.
• Negative numbers are less than zero.
• When subtracting larger numbers from smaller ones, the result is negative.

In the given exercise, recognize that -121 is a large negative number. When comparing it to positive 36 (found from adding 2 and 34), you realize that subtracting 121 is equivalent to adding the opposite of 121.
This switches the perspective to altering 36 with a negative influence, resulting in a total of -85. Practicing these principles further cements understanding, helping you tackle more complex algebraic expressions with confidence.