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Chapter 3: Problem 45

Fill in the blank with the appropriate number. $$ ______ -100=0$$

Short Answer

Expert verified
100

Step by step solution

01

Understand the problem

We need to find the number that, when subtracted by 100, equals 0.
02

Set up the equation

Let the unknown number be represented by 'x'. The equation can be written as: \[ x - 100 = 0 \]
03

Solve the equation

Add 100 to both sides of the equation to isolate the variable 'x': \[ x - 100 + 100 = 0 + 100 \] Simplifying this, we get: \[ x = 100 \]
04

Verify the solution

Substitute 'x' back into the original equation to ensure it holds true: \[ 100 - 100 = 0 \] This verifies that the solution is correct.

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Key Concepts

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

solving equations
Solving equations is a fundamental concept in algebra. It involves finding the value of a variable that makes the equation true. An equation is like a balance; whatever you do to one side, you must do to the other to keep it balanced. For instance, in the exercise, we started with the equation \[ x - 100 = 0 \] To solve for the variable 'x', we added 100 to both sides of the equation. This isolated the variable on one side: \[ x - 100 + 100 = 0 + 100 \] Simplifying, we got: \[ x = 100 \] By isolating the variable, we effectively solved the equation.
addition
Addition is one of the primary operations in algebra. It's all about combining numbers to get a new total. In our exercise, we used addition to isolate the variable 'x': \[ x - 100 + 100 = 0 + 100 \] Here, adding 100 to both sides helped balance the equation while isolating the variable. Addition is used frequently in algebra to move terms from one side of an equation to the other.
Remember: whatever you add to one side, you must also add to the other side to maintain equality.
variables
Variables are symbols that represent unknown values. In algebra, we often use letters like 'x', 'y', or 'z' as variables. In the given exercise, 'x' was our variable. We needed to find its value so that the equation \[ x - 100 = 0 \] would be true. When solving for a variable, our goal is to isolate it on one side of the equation. This allows us to determine its value. Variables play a crucial role in algebra as they make it possible to write general equations and solve for unknowns.
subtraction
Subtraction is a key operation in algebra, frequently used to simplify expressions and solve equations. In the provided exercise, the subtraction was already present in the equation: \[ x - 100 = 0 \] To solve, we had to 'undo' the subtraction by using addition. By adding 100 to both sides, we canceled out the -100: \[ x - 100 + 100 = 0 + 100 \] Simplifying, we obtained: \[ x = 100 \] Subtraction can be thought of as 'taking away' and is often reversed by addition to balance equations.

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