Question
What is the inverse operation?
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Answer
okay use x/4=12 as an exapmle
Answered by
GPT-4o mini
The term "inverse operation" refers to a mathematical operation that reverses the effect of another operation. Here are a few examples:
1. **Addition and Subtraction**: The inverse operation of addition is subtraction. If you have an equation like \( x + 5 = 10 \), you can use subtraction to find \( x \) by subtracting 5 from both sides: \( x = 10 - 5 \).
2. **Multiplication and Division**: The inverse operation of multiplication is division. For example, if you have \( 4x = 20 \), you can divide both sides by 4 to solve for \( x \): \( x = \frac{20}{4} \).
3. **Exponentiation and Root Extraction**: The inverse operation of exponentiation is taking the root. For instance, if \( y = x^2 \), then \( x \) can be found using the square root: \( x = \sqrt{y} \).
Inverse operations are fundamental in solving equations and understanding the relationships between different mathematical operations.
1. **Addition and Subtraction**: The inverse operation of addition is subtraction. If you have an equation like \( x + 5 = 10 \), you can use subtraction to find \( x \) by subtracting 5 from both sides: \( x = 10 - 5 \).
2. **Multiplication and Division**: The inverse operation of multiplication is division. For example, if you have \( 4x = 20 \), you can divide both sides by 4 to solve for \( x \): \( x = \frac{20}{4} \).
3. **Exponentiation and Root Extraction**: The inverse operation of exponentiation is taking the root. For instance, if \( y = x^2 \), then \( x \) can be found using the square root: \( x = \sqrt{y} \).
Inverse operations are fundamental in solving equations and understanding the relationships between different mathematical operations.
Answered by
GPT-4o mini
Sure! Let's use the equation \( \frac{x}{4} = 12 \) to demonstrate the concept of inverse operations.
1. **Identify the operation**: In this equation, \( \frac{x}{4} \) means that \( x \) is being divided by 4.
2. **Find the inverse operation**: The inverse operation of division is multiplication.
3. **Apply the inverse operation**: To isolate \( x \), multiply both sides of the equation by 4:
\[
\frac{x}{4} \times 4 = 12 \times 4
\]
This simplifies to:
\[
x = 48
\]
So, the solution to the equation \( \frac{x}{4} = 12 \) is \( x = 48 \).
In summary, by using the inverse operation (multiplication), we've successfully solved for \( x \).
1. **Identify the operation**: In this equation, \( \frac{x}{4} \) means that \( x \) is being divided by 4.
2. **Find the inverse operation**: The inverse operation of division is multiplication.
3. **Apply the inverse operation**: To isolate \( x \), multiply both sides of the equation by 4:
\[
\frac{x}{4} \times 4 = 12 \times 4
\]
This simplifies to:
\[
x = 48
\]
So, the solution to the equation \( \frac{x}{4} = 12 \) is \( x = 48 \).
In summary, by using the inverse operation (multiplication), we've successfully solved for \( x \).
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