Question

假设 $a \ast b$ 表示 $3a - b$ 。若下式成立，那么 $x$ 的值是多少？ $2 \ast (5 \ast x) = 1\text{？}$

Suppose that $a \ast b$ means $3a - b.$ What is the value of $x$ if $2 \ast (5 \ast x) = 1?$

$\dfrac{1}{10}$

$2$

$\dfrac{10}{3}$

$10$

$14$

先化简内部运算 $5\ast x$

Start by simplifying the inner operation $5\ast x$ .

从内到外两次应用定义 $a\ast b=3a-b$

Apply the definition $a\ast b=3a-b$ twice, from the inside out.

Click to load, then click again to play

先算内层运算，得 $5\ast x=15-x$ 。再应用一次定义： $\begin{aligned} 2\ast(15-x)&=6-(15-x)\\ &=x-9\text{。} \end{aligned}$ 因此 $x-9=1$ ，所以 $x=10$ 。

所以正确答案是 D。

First, $5\ast x=15-x$ . Applying the operation again gives $\begin{aligned} 2\ast(15-x)&=6-(15-x)\\ &=x-9. \end{aligned}$ Thus $x-9=1$ , so $x=10$ .

Thus, D is the correct answer.