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

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 \(y\).

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.

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: \[ 2(5y - 5) + 13 = 10y + 9 \]

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

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

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

Final Answer