Consider the equation \( 6 y+13=\ldots+8 \). Which value or expression can you write in the blank so the equat has no solution? 0 13 \( 5 y \)
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To create a scenario where the equation \(6y + 13 = \ldots + 8\) has no solution, you would want the left-hand side to never equal the right-hand side. If you set the blank to a number that contradicts the required equality, you can achieve this. For example, filling in the blank with \(5y\) would give \(6y + 13 = 5y + 8\). Rearranging this results in \(y + 13 = 8\), leading to \(y = -5\). However, if you place a constant such as 13 in the blank, you'd have \(6y + 13 = 13 + 8\), which simplifies to \(6y = 8\), yielding a valid solution. Thus, if you put in a value like \(5y + 10\), the equation would become \(6y + 13 = 5y + 10 + 8\) simplifying to \(6y + 13 = 5y + 18\), which leads to \(y = 5\) – a valid solution. So, using a value that leads to a contradiction can ensure the equation remains unsolved!
