Calculating linear equations involves a series of steps to isolate the variable and find its value. The process, in essence, involves manipulating the equation to get the variable by itself on one side of the equals sign.
Steps to Solve Linear Equations
Here's a detailed breakdown of how to solve linear equations, incorporating the steps provided in the references:
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Simplify Both Sides:
- The first step is to simplify each side of the equation independently.
- This involves combining any like terms on the same side of the equal sign.
- For example, if you have an equation like 2x + 3 + x = 10, combine '2x' and 'x' to get '3x + 3 = 10'.
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Combine Opposite-Side Like Terms:
- Next, you want to bring all the variable terms to one side of the equation and all the constant terms to the other side.
- You do this by performing inverse operations. For example, if you have '3x + 3 = 10', subtract 3 from both sides to get '3x = 7'.
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Isolate the Variable:
- Once you have a single variable term on one side and a constant term on the other, isolate the variable.
- You do this by dividing or multiplying both sides of the equation by the coefficient of the variable. In the example, divide both sides of '3x = 7' by 3, which gives you 'x = 7/3'.
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Check Your Answer:
- After obtaining your solution, plug the value you found for the variable back into the original equation.
- If both sides of the equation remain balanced (equal), your answer is correct. This ensures there were no mistakes during the solving process.
Example
Let's walk through an example to demonstrate these steps:
Problem: Solve for x: 5x + 2 = 3x + 8
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Simplify Both Sides: The equation is already simplified on both sides.
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Combine Opposite-Side Like Terms:
- Subtract 3x from both sides: 5x - 3x + 2 = 3x - 3x + 8 This simplifies to 2x + 2 = 8
- Subtract 2 from both sides: 2x + 2 - 2 = 8 - 2. This simplifies to 2x = 6
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Isolate the Variable:
- Divide both sides by 2: 2x / 2 = 6 / 2. This results in x = 3
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Check the Answer:
- Plug x = 3 back into the original equation: 5(3) + 2 = 3(3) + 8
- Simplify: 15 + 2 = 9 + 8. This is 17 = 17, so the solution is correct.
Tips For Success
- Keep track of your work: Write down each step clearly, it can help avoid mistakes.
- Perform inverse operations: Remember to use the inverse operation to move terms across the equal sign (e.g., addition/subtraction, multiplication/division).
- Be careful with signs: Pay close attention to positive and negative signs.
- Practice: The more you practice, the better you will become at solving equations.
By following these steps, you can successfully calculate linear equations.
