TMUA Viluxent Set 1 Paper 2 · Question 10

Consider the following attempt to solve the equation $|x-3|=2x+1$ :

\begin{aligned} \text{(I)}\quad &|x-3|=2x+1\\ \text{(II)}\quad &(x-3)^2=(2x+1)^2\\ \text{(III)}\quad &x^2-6x+9=4x^2+4x+1\\ \text{(IV)}\quad &0=3x^2+10x-8\\ \text{(V)}\quad &0=(3x-2)(x+4)\\ \text{(VI)}\quad &x=\tfrac23\text{ or }x=-4. \end{aligned}

The solutions of the original equation are concluded to be $x=\frac23$ and $x=-4$ .

Which one of the following is true?

AThe conclusion is entirely correct.

BThe conclusion is not entirely correct; the first error occurs in passing from (I) to (II).

CThe conclusion is not entirely correct; the first error occurs in passing from (II) to (III).

DThe conclusion is not entirely correct; the first error occurs in passing from (III) to (IV).

EThe conclusion is not entirely correct; the first error occurs in passing from (IV) to (V).

FThe conclusion is not entirely correct; the first error occurs in passing from (V) to (VI).

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