To rearrange formulas to isolate a specific variable, you perform inverse operations on both sides of the equation until the desired variable is by itself on one side. The goal is to "undo" whatever operations are being performed on the variable you want to isolate.
Steps to Isolate a Variable
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Identify the Variable: Determine which variable you need to isolate.
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Inverse Operations: Use inverse operations to isolate the variable. Remember to apply the operation to both sides of the equation to maintain balance.
- Addition and Subtraction: If a term is added to the variable, subtract it from both sides. If a term is subtracted, add it to both sides.
- Multiplication and Division: If the variable is multiplied by a factor, divide both sides by that factor. If the variable is divided by a factor, multiply both sides by that factor.
Example
Let's say we have the formula for the area of a triangle:
A = (1/2) * b * hWhere:
- A = Area
- b = Base
- h = Height
If we want to isolate 'h' (height), we can follow these steps (as illustrated by Khan Academy):
- Original Equation:
A = (1/2) * b * h - Multiply both sides by 2: This gets rid of the (1/2).
2A = b * h - Divide both sides by 'b': This isolates 'h'.
2A / b = h - Result:
h = 2A / b
So, we have successfully isolated 'h'. According to the Khan Academy video, to isolate 'h', we can divide both sides of the equation by 'b' because 'b' is multiplying 'h'.
Key Considerations
- Maintain Balance: Whatever operation you perform on one side of the equation, you must perform on the other side to keep the equation balanced.
- Order of Operations: Think about the order of operations (PEMDAS/BODMAS) in reverse when isolating variables. Undo addition/subtraction before multiplication/division.
- Complex Formulas: Some formulas may require multiple steps or more advanced algebraic techniques (like factoring or completing the square) to isolate the variable.
