Solving algebraic equations with fractions in Grade 9 involves similar steps as solving regular algebraic equations, but with extra attention to handling the fractions. The key is to eliminate the fractions to simplify the equation. Here's a breakdown:
Steps to Solve Algebraic Equations with Fractions
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Identify the Fractions: Pinpoint all the terms in the equation that are fractions.
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Find the Least Common Denominator (LCD): Determine the LCD of all the fractions in the equation.
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Multiply Every Term by the LCD: Multiply every term on both sides of the equation by the LCD. This is the crucial step to eliminate the fractions.
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Simplify: After multiplying by the LCD, simplify both sides of the equation. The fractions should now be eliminated.
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Solve the Remaining Equation: You will now have a simpler algebraic equation without fractions. Use standard algebraic techniques (addition, subtraction, multiplication, division) to isolate the variable and solve for its value.
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Check Your Solution: Substitute your solution back into the original equation (with fractions) to verify that it makes the equation true. This is an important step to catch any errors made during the solving process.
Example
Let's consider an example based on the reference provided (0:30-0:40):
Solve for x: x/4 + 2 = 7
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Identify fractions: The fraction is x/4.
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Find the LCD: The LCD is 4.
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Multiply every term by the LCD: 4 (x/4) + 4 2 = 4 * 7
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Simplify: x + 8 = 28
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Solve the remaining equation:
- Subtract 8 from both sides: x = 20
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Check your solution: 20/4 + 2 = 5 + 2 = 7. The solution is correct.
Tips for Success
- Pay Attention to Signs: Be careful with negative signs when multiplying and simplifying.
- Distribute Properly: Make sure to distribute the LCD to every term in the equation.
- Double-Check Your Work: It's easy to make mistakes when dealing with fractions, so take your time and double-check each step.
- Practice: The more you practice, the more comfortable you'll become with solving algebraic equations with fractions.
