1. **State the problem:** We need to find the value of the constant $a$ given that the coefficient of $x$ in the expansion of $(2 + ax)^3$ is 96. 2. **Recall the binomial expansion formula:** $$(x + y)^n = \sum_{k=0}^n \binom{n}{k} x^{n-k} y^k$$ 3. **Apply the formula to $(2 + ax)^3$:** $$(2 + ax)^3 = \binom{3}{0} 2^3 (ax)^0 + \binom{3}{1} 2^2 (ax)^1 + \binom{3}{2} 2^1 (ax)^2 + \binom{3}{3} 2^0 (ax)^3$$ 4. **Simplify each term:** - $\binom{3}{0} 2^3 (ax)^0 = 1 \times 8 \times 1 = 8$ - $\binom{3}{1} 2^2 (ax)^1 = 3 \times 4 \times a x = 12 a x$ - $\binom{3}{2} 2^1 (ax)^2 = 3 \times 2 \times a^2 x^2 = 6 a^2 x^2$ - $\binom{3}{3} 2^0 (ax)^3 = 1 \times 1 \times a^3 x^3 = a^3 x^3$ 5. **Identify the coefficient of $x$:** The coefficient of $x$ is $12 a$. 6. **Set the coefficient equal to 96 and solve for $a$:** $$12 a = 96$$ $$a = \frac{96}{12} = 8$$ **Final answer:** The value of the constant $a$ is $8$.