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sleet_krkn [62]
4 years ago
15

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

Mathematics
2 answers:
Rudiy274 years ago
8 0
(2 / x-1)> (7 / x + 1)
 For this case we can solve the problem graphically.
 The solution will be the shaded region.
 Note: see attached image.
 Answer:
 The solution is given by:1 <x <9/5

nika2105 [10]4 years ago
4 0

Answer:

Given inequality,

\frac{2}{x} - 1 > \frac{7}{x} + 1

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

\frac{2}{x} > \frac{7}{x}+2

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

\frac{2}{x}-\frac{7}{x} > 2

\frac{2-7}{x} > 2

-\frac{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 -\frac{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 -\frac{5}{2} < x

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