Class 7 Exam > Class 7 Questions > Find y6y-2/9+3y+5/18=1/3?
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6y-2/9+3y+5/18=1/3?
6y-2/9+3y+5/18=1/3?
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Find y6y-2/9+3y+5/18=1/3?
To solve the equation \( \frac{6y - 2}{9} + \frac{3y + 5}{18} = \frac{1}{3} \), follow these steps:
Step 1: Simplify the fractions
- To simplify the equation, find a common denominator for the fractions. The common denominator for 9 and 18 is 18.
- Rewrite \( \frac{6y - 2}{9} \) as \( \frac{2(6y - 2)}{18} = \frac{12y - 4}{18} \).
- The equation now looks like this:
Step 2: Combine the fractions
- Combine the left-hand side:
Step 3: Eliminate the fraction
- Cross-multiply to eliminate the fraction:
Step 4: Distribute and simplify
- Distributing gives:
- Subtract 3 from both sides:
Step 5: Solve for y
- Divide both sides by 45:
Conclusion
- The solution to the equation is:
Step 1: Simplify the fractions
- To simplify the equation, find a common denominator for the fractions. The common denominator for 9 and 18 is 18.
- Rewrite \( \frac{6y - 2}{9} \) as \( \frac{2(6y - 2)}{18} = \frac{12y - 4}{18} \).
- The equation now looks like this:
- \( \frac{12y - 4}{18} + \frac{3y + 5}{18} = \frac{1}{3} \)
Step 2: Combine the fractions
- Combine the left-hand side:
- \( \frac{12y - 4 + 3y + 5}{18} = \frac{1}{3} \)
- \( \frac{15y + 1}{18} = \frac{1}{3} \)
Step 3: Eliminate the fraction
- Cross-multiply to eliminate the fraction:
- \( 3(15y + 1) = 18 \)
Step 4: Distribute and simplify
- Distributing gives:
- \( 45y + 3 = 18 \)
- Subtract 3 from both sides:
- \( 45y = 15 \)
Step 5: Solve for y
- Divide both sides by 45:
- \( y = \frac{15}{45} = \frac{1}{3} \)
Conclusion
- The solution to the equation is:
- \( y = \frac{1}{3} \)
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Find y6y-2/9+3y+5/18=1/3?
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Find y6y-2/9+3y+5/18=1/3? for Class 7 2024 is part of Class 7 preparation. The Question and answers have been prepared according to the Class 7 exam syllabus. Information about Find y6y-2/9+3y+5/18=1/3? covers all topics & solutions for Class 7 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find y6y-2/9+3y+5/18=1/3?.
Find y6y-2/9+3y+5/18=1/3? for Class 7 2024 is part of Class 7 preparation. The Question and answers have been prepared according to the Class 7 exam syllabus. Information about Find y6y-2/9+3y+5/18=1/3? covers all topics & solutions for Class 7 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find y6y-2/9+3y+5/18=1/3?.
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