The solution of |2 (x – 4) |>1 where x 4 is: - Vidyadip

MCQ

The solution of $\Big|\frac{2}{(\text{x} – 4)}\Big|>1$ where $\text{x}\neq4$ is:

A
$(2, 6)$
✓
$(2, 4)\cup(4, 6)$
C
$(2, 4)\cup(4,\infty)$
D
$(-\infty, 4)\cup(4, 6)$

✓

Answer

Correct option: B.

$(2, 4)\cup(4, 6)$

Given,$\Big|\frac{2}{(\text{x} – 4)}\Big|>1$
$\Rightarrow2 > |\text{x} – 4|$
$\Rightarrow |\text{x} – 4|<2$
$\Rightarrow-2<\text{x}-4<2$
$\Rightarrow-2+4 < \text{x} < 2+4$
$\Rightarrow2<\text{x}<6$
$\Rightarrow\text{x}\in(2, 6),$
where $\text{x}\neq4$
$\Rightarrow\text{x}\in(2, 4)\cup(4, 6)$

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