Let's solve the equation \( 5x - 3(x - 2) = 8 \) step-by-step to determine whose solution is correct.
Starting with the given equation:
\[ 5x - 3(x - 2) = 8 \]
Now, distribute \(-3\) across \((x - 2)\):
\[ 5x - 3x + 6 = 8 \]
Combine like terms \(5x - 3x\):
\[ 2x + 6 = 8 \]
Next, isolate \(x\) by subtracting \(6\) from both sides:
\[ 2x = 8 - 6 \]
This simplifies to:
\[ 2x = 2 \]
Now, divide both sides by \(2\):
\[ x = 1 \]
So, the correct solution is \(x = 1\), which means Lisa is correct and Austin made a mistake in his calculations.