TMUA 2018 · Paper 2 · Question 9

Consider the following attempt to solve the equation $4 x 2 x - 1 = 10 x - 5$ :

4 x 2 x - 1 = 10 x - 5

$↓$ (I)

4 x 2 x - 1 = 5 (2 x - 1)

$↓$ (II)

16 x^{2} (2 x - 1) = 25 (2 x - 1)^{2}

$↓$ (III)

16 x^{2} = 25 (2 x - 1)

$↓$ (IV)

16 x^{2} - 50 x + 25 = 0

$↓$ (V)

(8 x - 5) (2 x - 5) = 0

$↓$ (VI)

The solutions of the original equation are $x = \frac{5}{8}$ and $x = \frac{5}{2}$ .

Which one of the following is true?