Question

What is the solution of (2/x-1)>(7/x+1)

Answer 1

Given inequality,

`(2)/(x) - 1 > (7)/(x) + 1`

Using the property a > b ⇒ a + c > b + c ∀ a, b, c ∈ R

`(2)/(x) > (7)/(x)+2`

Using the property a > b ⇒ a - c > b - c ∀ a, b, c ∈ R

`(2)/(x)-(7)/(x) > 2`

`(2-7)/(x) > 2`

`-(5)/(x) > 2`

Case 1 : If x > 0 ⇒ -x < 0

∵ a > b ⇒ ca < cb if c < 0,

`\implies 5 < -2x`

Now, -1/2 < 0

`\implies -(5)/(2) > x`

Case 2 : If x < 0 ⇒ -x > 0

∵ a > b ⇒ ca > cb if c > 0,

`\implies 5 > -2x`

Now, -1/2 < 0

`\implies -(5)/(2) < x`