Step 1 :\( \lim_{x \to 1} \frac{2x^2 - 2}{x - 1} = 3a - 1 \)
Step 2 :\( \lim_{x \to 1} \frac{2(x^2 - 1)}{x - 1} = 3a - 1 \)
Step 3 :\( \lim_{x \to 1} \frac{2(x - 1)(x + 1)}{x - 1} = 3a - 1 \)
Step 4 :\( \lim_{x \to 1} 2(x + 1) = 3a - 1 \)
Step 5 :\( 2(1 + 1) = 3a - 1 \)
Step 6 :\( 4 = 3a - 1 \)
Step 7 :\( a = \frac{5}{3} \)