# Solve the following system of inequalities 2x+17x-1>5,x+7x-8>2 - Mathematics

Sum

Solve the following system of inequalities (2x + 1)/(7x - 1) > 5, (x + 7)/(x - 8) > 2

#### Solution

(2x + 1)/(7x - 1) > 5

Subtracting 5 both side, we get

(2x + 1)/(7x - 1) - 5 > 0

⇒ (2x + 1- 35x + 5)/(7x - 1) > 0

⇒ (6 - 33x)/(7x - 1) > 0

For above fraction be greater than 0, either both denominator and numerator should be greater than 0 or both should be less than 0.

⇒ 6 – 33x > 0 and 7x – 1 > 0

⇒ 33x < 6 and 7x > 1

⇒ x < 2/11 and x > 1/7

⇒ 1/7 < x < 2/11  ......(i)

Or

⇒ 6 – 33x < 0 and 7x – 1 < 0

⇒ 33x > 6 and 7x < 1

⇒ x > 2/11 and x < 1/7

⇒ 2/11< x < 1/7   ......(Which is not possible since 1/7 > 2/11)

Also, (x + 7)/(x - 8) > 2

Subtracting 2 both sides, we get

⇒ (x + 7)/(x - 8) - 2 > 0

⇒ (x + 7 - 2x + 16)/(x - 8) > 0

⇒ (23 - x)/(x - 8) > 0

For above fraction be greater than 0.

Either both denominator and numerator should be greater than 0 or both should be less than 0.

⇒ 23 – x > 0 and x – 8 > 0

⇒ x < 23 and x > 8

⇒ 8 < x < 23   ......(ii)

Or

23 – x < 0 and x – 8 < 0

⇒ x > 23 and x < 8

⇒ 23 < x < 8   ......(Which is not possible, as 23 > 8]

Therefore, from equations (i) and (ii).

We infer that there is no solution satisfying both inequalities.

Hence, the given system has no solution.

Concept: Solution of System of Linear Inequalities in Two Variables
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Chapter 6: Linear Inequalities - Exercise [Page 108]

#### APPEARS IN

NCERT Mathematics Exemplar Class 11
Chapter 6 Linear Inequalities
Exercise | Q 13 | Page 108

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