Inverse Operations
Apply inverse operations in Grade 9 algebra to isolate variables: undo addition with subtraction, multiplication with division, and exponents with roots to solve equations step by step.
Key Concepts
Property Inverse operations are operations that undo each other. For example: Addition $\longleftrightarrow$ Subtraction.
Examples $In x + 9 = 14$, use the inverse of addition (subtraction): $x = 14 9$, so $x = 5.$ $In y 7 = 3$, use the inverse of subtraction (addition): $y = 3 + 7$, so $y = 10.$.
Explanation Think of inverse operations as an 'undo' button for math. If an equation has addition, you use subtraction to cancel it out and get the variable by itself. If it has subtraction, you use addition! It is like putting on your shoes (addition) and taking them off (subtraction)—one action reverses the other to get you back where you started.
Common Questions
What are inverse operations in algebra?
Inverse operations undo each other. The pairs are: addition and subtraction, multiplication and division, and raising to a power and taking a root. Using inverse operations isolates the variable to solve equations.
How do inverse operations help solve multi-step equations?
Work in reverse order of operations (PEMDAS backwards). If an equation has 2x + 5 = 13, first undo the addition by subtracting 5 from both sides to get 2x = 8, then undo multiplication by dividing both sides by 2 to get x = 4.
Why must you apply inverse operations to both sides of an equation?
An equation is a balance — both sides are equal. Applying an operation to only one side destroys that balance. Performing the same inverse operation on both sides keeps the equation true while isolating the variable.