Solving an algebraic expression generally means finding the value of an unknown variable. Here's a breakdown of how to approach it, based on solving algebraic equations for a single variable:
Understanding Algebraic Equations
An algebraic equation is a mathematical statement that shows the equality of two expressions. These expressions can contain numbers, variables, and mathematical operations. The goal is typically to isolate the variable on one side of the equation to determine its value.
Steps to Solve Algebraic Equations
Here's a general approach, illustrated with an example inspired by the YouTube video "Algebra - How To Solve Equations Quickly!":
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Isolate the Variable: The primary goal is to get the variable by itself on one side of the equation.
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Perform Inverse Operations: Use inverse operations to undo the operations affecting the variable. Remember to apply the same operation to both sides of the equation to maintain balance.
- Addition and Subtraction: If a number is added to the variable, subtract that number from both sides. If a number is subtracted, add it to both sides.
- Multiplication and Division: If the variable is multiplied by a number, divide both sides by that number. If the variable is divided by a number, multiply both sides by that number.
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Example: Solve for x in the equation 3x = 12.
- The variable x is being multiplied by 3.
- The opposite of multiplication is division.
- Divide both sides of the equation by 3:
3x/3 = 12/3 - This simplifies to x = 4. Therefore, the answer is 4 (as demonstrated in the reference).
Summary
| Step | Action | Example |
|---|---|---|
| 1. Identify the Variable | Determine which variable you are solving for. | x in the equation 3x = 12 |
| 2. Isolate the Term | Use addition or subtraction to isolate the term containing the variable. | N/A (already isolated in this example) |
| 3. Use Inverse Operations | Apply multiplication or division to isolate the variable completely. Remember to do it to both sides. | Divide both sides of 3x = 12 by 3. |
| 4. Simplify | Perform the calculations to find the value of the variable. | x = 4 |
