# NCERT Class 11-Math's: Chapter –6 Linear Inequalities Part 6

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**Question 9:**

A solution of acid is to be diluted by adding acid solution to it. The resulting mixture is to be more than but less than acid. If there is litres of the solution, how many litres of solution will have to be added?

**Answer:**

More than litres but less than litres.

**Question 10:**

A solution is to be kept between and . What is the range of temperature in degree Fahrenheit, if the conversion formula is ?

**Answer:**

Between and

**Question 11:**

The longest side of a triangle is twice the shortest side and the third side is longer than the shortest side. If the perimeter of the triangle is more than then find the minimum length of the shortest side.

**Answer:**

**Question 12:**

In drilling world’s deepest hole it was found that the temperature T in degree Celsius, *x* km below the earth’s surface was given by . At what depth will the temperature be between and ?

**Answer:**

Between and

**Long Answer Type**

**Question 13:**

Solve the following system of inequalities

**Answer:**

Given,

Subtracting 5 both side, we get

Hence, for above fraction be greater than , either both denominator and numerator should be greater than or both should be less than

Or

Also,

Subtracting 2 both sides, we get

Hence, for above fraction be greater than 0, either both denominator and numerator should be greater than 0 or both should be less than 0

and

Or

and

and

From [1] and [2], it is clear that there is no solution satisfying both inequalities, hence the given system has no solution

**Question 14:**

Find the linear inequalities for which the shaded region in the given figure is the solution set.

**Answer:**