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Questions and Answers
What are inverse operations?
What are inverse operations?
- Operations that always produce a different result
- 2 operations that will be performed on a number or variable, resulting in the original number or variable (correct)
- Operations that can only be performed on variables
- None of the above
Undo and inverse operations are the same.
Undo and inverse operations are the same.
True (A)
What are the four kinds of inverse operation pairs?
What are the four kinds of inverse operation pairs?
Addition and subtraction, multiplication and division, squares and square roots, cubes and cube roots.
What is the solution for the equation x + 2 = 3?
What is the solution for the equation x + 2 = 3?
What is the solution for the equation x - 2 = 3?
What is the solution for the equation x - 2 = 3?
What is the solution for the equation 2x = 8?
What is the solution for the equation 2x = 8?
What is the solution for the equation x / 2 = 8?
What is the solution for the equation x / 2 = 8?
What is the solution for the equation 3(x - 2) = 12?
What is the solution for the equation 3(x - 2) = 12?
What are the possible values of x in the equation x^2 = 9?
What are the possible values of x in the equation x^2 = 9?
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Study Notes
Inverse Operations
- Inverse operations are two operations performed on a number or variable, resulting in the original value.
- They are essential in solving equations by reversing actions to isolate the variable.
Concept of Undoing
- The concept of "undo" refers to the action of performing two inverse operations consecutively to return to the original number or variable.
Pairs of Inverse Operations
- Key pairs of inverse operations include:
- Addition and subtraction
- Multiplication and division
- Squares and square roots (applicable only for positive numbers)
- Cubes and cube roots
Application of Inverse Operations in Equations
- To solve x + 2 = 3 using addition, subtract 2 from both sides, yielding x = 1.
- For x - 2 = 3, add 2 to both sides to find x = 5.
- In the equation 2x = 8, divide both sides by 2 to solve for x, resulting in x = 4.
- To solve x/2 = 8, multiply both sides by 2, giving x = 16.
Example Problem Solving
- For the equation 3(x - 2) = 12, first divide both sides by 3 to simplify, yielding x - 2 = 4. Then, add 2 to find x = 6.
- For x^2 = 9, take the square root of both sides to find x = (+/-) 3, indicating two possible solutions.
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