Questions: How many solutions does the following equation have? 7(y-8)=7 y+42 Choose 1 answer: (A) No solutions (B) Exactly one solution (C) Infinitely many solutions

Solution Steps

To determine the number of solutions to the equation \( 7(y-8) = 7y + 42 \), we need to simplify and solve it. First, distribute the 7 on the left side, then combine like terms and see if the equation holds true for all values of \( y \), no values of \( y \), or a specific value of \( y \).

We start with the equation: \[ 7(y - 8) = 7y + 42 \] Distributing the \(7\) on the left side gives: \[ 7y - 56 = 7y + 42 \]

Next, we subtract \(7y\) from both sides: \[ 7y - 7y - 56 = 42 \] This simplifies to: \[ -56 = 42 \]

The equation \(-56 = 42\) is a contradiction, meaning there are no values of \(y\) that can satisfy the equation. Therefore, the equation has no solutions.

Final Answer