Questions: (4y-6)/4 + 13/8 = (8y+1)/8

Solution Steps

To solve the equation $\frac{4 y-6}{4}+\frac{13}{8}=\frac{8 y+1}{8}$, we can follow these steps:

1. Find a common denominator for all the fractions involved.
2. Combine the fractions on the left-hand side.
3. Simplify the equation to isolate the variable \( y \).

To solve the equation \(\frac{4y-6}{4} + \frac{13}{8} = \frac{8y+1}{8}\), we first find a common denominator for all the fractions. The common denominator for 4 and 8 is 8.

Rewrite each term with the common denominator: \[ \frac{4y-6}{4} = \frac{2(4y-6)}{8} = \frac{8y-12}{8} \] So the equation becomes: \[ \frac{8y-12}{8} + \frac{13}{8} = \frac{8y+1}{8} \]

Combine the fractions on the left-hand side: \[ \frac{8y-12 + 13}{8} = \frac{8y+1}{8} \] Simplify the numerator: \[ \frac{8y + 1}{8} = \frac{8y + 1}{8} \]

Since both sides of the equation are equal, the equation holds for all values of \( y \). This means that the equation is an identity and there are infinitely many solutions.

Final Answer