Solve the system of equations in R.|x – 2|/(x – 2) > 0

1.	Solve the system of equations in R.\|x – 2\|/(x – 2) > 0
Answer» Given as \|x – 2\|/(x – 2) > 0 Clearly it states, x ≠ 2 therefore two case arise: Case 1: x – 2 > 0 x > 2 Now, in this case \|x – 2\| = x – 2 x ϵ (2, ∞)….(1) Case 2: x – 2 < 0 x < 2 In this case, \|x – 2\|= – (x – 2) – (x – 2)/(x – 2) > 0 – 1 > 0 Here, Inequality doesn’t get satisfy This case gets nullified. ∴ x ∈ (2, ∞) from (1)

Answer»

Given as

|x – 2|/(x – 2) > 0

Clearly it states, x ≠ 2 therefore two case arise:

Case 1: x – 2 > 0

x > 2

Now, in this case |x – 2| = x – 2

x ϵ (2, ∞)….(1)

Case 2: x – 2 < 0

x < 2

In this case, |x – 2|= – (x – 2)

– (x – 2)/(x – 2) > 0

– 1 > 0

Here, Inequality doesn’t get satisfy

This case gets nullified.

∴ x ∈ (2, ∞) from (1)

Discussion