To find the value of \( n \) that makes the equation \( 4(0.5n-3)=-0.25(12-8n) \) true, we need to solve the equation step by step:
1. Start by simplifying both sides of the equation:
\( 4(0.5n-3) = -0.25(12-8n) \)
\( 2n - 12 = -3 + 2n \) (distributing and simplifying)
2. Rearrange the equation to isolate \( n \) on one side:
\( 2n - 12 = 2n - 3 \)
\( 2n - 2n = -3 + 12 \)
\( 0 = 9 \)
Since the equation simplifies to \( 0 = 9 \), this means that the equation is inconsistent, and there is no value of \( n \) that makes the equation true.
Therefore, the answer to the question "What value of \( n \) makes the equation \( 4(0.5n-3)=-0.25(12-8n) \) true?" is that there is no such value of \( n \) that satisfies the equation.
