To solve the equation \( 7(1.5n - 4) = 0.5(n + 15) \), we first simplify each side.
Start by distributing on the left side: \[ 7 \cdot 1.5n - 7 \cdot 4 = 10.5n - 28 \] So the left side becomes: \[ 10.5n - 28 \]
Now, distribute on the right side: \[ 0.5n + 0.5 \cdot 15 = 0.5n + 7.5 \]
Now we can rewrite the equation: \[ 10.5n - 28 = 0.5n + 7.5 \]
Next, we will isolate \(n\). First, subtract \(0.5n\) from both sides: \[ 10.5n - 0.5n - 28 = 7.5 \] \[ 10n - 28 = 7.5 \]
Now, add 28 to both sides: \[ 10n = 7.5 + 28 \] \[ 10n = 35.5 \]
Finally, divide both sides by 10 to solve for \(n\): \[ n = \frac{35.5}{10} \] \[ n = 3.55 \]
Thus, the solution to the equation is: \[ \boxed{3.55} \]
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