To solve a linear equation in one variable, you need to isolate the variable on one side of the equation. Here's a step-by-step guide:
Steps to Solving a Linear Equation in One Variable
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Simplify Each Side:
- If required, simplify each side of the equation first.
- Use the distributive property to eliminate parentheses. For example, 2(x + 3) becomes 2x + 6.
- Combine like terms on each side of the equation. For example, 3x + 2x becomes 5x.
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Isolate the Variable Term:
- The goal is to have the term containing the variable alone on one side of the equals sign.
- To do this, use the addition or subtraction property of equality. This means adding or subtracting the same number from both sides of the equation.
- For example, to get rid of a number being added to the variable side like x + 5 = 10, you subtract 5 from both sides to get x = 5.
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Isolate the Variable:
- Now, isolate the variable itself. If the variable is being multiplied by a number, divide by that number on both sides of the equation. If it's being divided, multiply by that number on both sides.
- For example, if you have 2x = 10, divide both sides by 2 to get x = 5.
Example
Let's solve this equation: 2(x + 3) - 4 = 12
| Step | Action | Equation |
|---|---|---|
| 1. Simplify the Left Side | Apply the distributive property | 2x + 6 - 4 = 12 |
| 2. Combine Like Terms | Combine constant terms | 2x + 2 = 12 |
| 3. Isolate Variable Term | Subtract 2 from both sides | 2x = 10 |
| 4. Isolate the Variable | Divide both sides by 2 | x = 5 |
Therefore, the solution to the equation is x = 5.
Summary of Steps
Here's a simplified breakdown:
- Simplify: Remove parentheses and combine like terms on each side.
- Isolate: Use addition/subtraction to get the variable term on one side and numbers on the other.
- Solve: Use multiplication/division to get the variable by itself.
By following these steps, you can confidently solve any linear equation in one variable.
