Questions: (5y-5)/3 + 13/6 = (10y+9)/6

(5y-5)/3 + 13/6 = (10y+9)/6

Solution

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Solution Steps

To solve the equation \(\frac{5y - 5}{3} + \frac{13}{6} = \frac{10y + 9}{6}\), we can follow these steps:

  1. Find a common denominator for all the fractions involved.
  2. Multiply through by the common denominator to clear the fractions.
  3. Simplify and solve the resulting linear equation for \(y\).
Step 1: Find a Common Denominator

To solve the equation \(\frac{5y - 5}{3} + \frac{13}{6} = \frac{10y + 9}{6}\), we first find a common denominator for all the fractions. The common denominator for 3 and 6 is 6.

Step 2: Clear the Fractions

Multiply every term by 6 to clear the fractions: \[ 6 \left( \frac{5y - 5}{3} \right) + 6 \left( \frac{13}{6} \right) = 6 \left( \frac{10y + 9}{6} \right) \] This simplifies to: \[ 2(5y - 5) + 13 = 10y + 9 \]

Step 3: Simplify the Equation

Distribute and combine like terms: \[ 10y - 10 + 13 = 10y + 9 \] \[ 10y + 3 = 10y + 9 \]

Step 4: Isolate the Variable

Subtract \(10y\) from both sides: \[ 3 = 9 \]

Step 5: Analyze the Result

The equation \(3 = 9\) is a contradiction, which means there is no value of \(y\) that satisfies the original equation.

Final Answer

\(\boxed{\text{No solution}}\)

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