Problem 65 - Prealgebra

Question

What number do you add to 8 to get \(3 ?\)

Step-by-Step Solution

Answer

Add -5 to 8 to get 3.

Step 1: Understand the Problem

We are asked to find the number that needs to be added to 8 to result in 3. We can represent this situation with an equation like this: 8 + x = 3.

Step 2: Setup the Equation

Write down the equation based on the problem statement. We have: 8 + x = 3.

Step 3: Isolate the Variable

To find the value of x, we need to get x by itself on one side of the equation. We can do this by subtracting 8 from both sides of the equation: 8 + x - 8 = 3 - 8.

Step 4: Simplify the Equation

Perform the subtraction on both sides of the equation: x = 3 - 8 x = -5.

Key Concepts

Prealgebra

Prealgebra is like the foundation of a building; it sets the groundwork for future learning in mathematics. It involves the basic concepts that prepare students for more advanced topics in algebra and beyond. Understanding these concepts is crucial because they help us make sense of the world using numbers and operations.
Prealgebra covers several key topics:

• Numbers: Learning about different types of numbers such as whole numbers, fractions, and decimals.
• Basic Operations: Understanding addition, subtraction, multiplication, and division.
• Equations and Variables: Introducing the idea of unknowns in mathematics, often represented as letters like x or y.
• Order of Operations: Knowing the rules for which operations to perform first in a mathematical expression.

In our exercise, we use prealgebra skills to set up and solve an equation involving addition, subtraction, and finding the unknown variable.

Addition and Subtraction

Addition and subtraction are two of the most fundamental arithmetic operations. They are used to combine or separate numbers. In our exercise, we are dealing with an equation where subtraction is used to solve for an unknown number.
Let's break it down further:

• Addition: This operation involves combining numbers to get a total or sum. For example, 8 + x = 3 indicates that when we add some number x to 8, we should get 3.
• Subtraction: This is the process of removing a number from another, which finds the difference. It's the opposite operation of addition. To isolate the unknown number x, we'll subtract 8 from both sides of the equation.

The solution to the equation uses subtraction to simplify our problem and determine that x must be -5, as subtracting gives the difference needed to achieve the set total of 3.

Inverse Operations

Inverse operations are pairs of mathematical operations that undo each other. Understanding this concept is vital for solving algebraic equations successfully. They help us manipulate equations and isolate variables to find their values.
In our specific exercise:

• Addition and Subtraction: They are inverse operations. If you know that 8 plus an unknown number equals 3, you can use subtraction to "undo" the addition and solve for the unknown.
• Using Inverses to Solve Equations: To find x in the equation 8 + x = 3, we subtract 8 (the inverse of addition) from both sides of the equation. This leaves us with x on one side and simplifies the equation.

By applying inverse operations, which in this case is subtraction, we can effectively find that the unknown number is -5. This method of using inverse operations is a crucial strategy widely used in solving all types of equations in mathematics.