Linear Inequalities - Online Test

et the marks scored by Rishi in the fourth paper be x.

Then 75≤95+72+83+x4<80⇒75≤250+x4<80

Multipling the inequality throughout by 4 ,we get

Let the length of the shortest piece be x cm.Then we have the length of the second and third pieces are x+3 and 2x centimeters respectively.

According to the question,

Hence the shortest piece may be atleast 8 cm long but it cannot be more than 22cm in length.

Let the consecutive odd natural numbers be x and x+2.

According to the question , x>10 and  x+(x+2)<40

Now x+(x+2)<40⇒2x<38⇒x<19

Hence the maximum value of x is 17 and minimum value is 11.

So the possible pairs of odd natural numbers are ( 11 , 13 ) , ( 13 , 15 ) , ( 15 , 17 ) , ( 17 , 19 )

Let x be the mark obtained by Rohit in the third test.

Then

65+70+x3≥65⇒135+x≥195⇒x≥60

Hence Rohit should get a minimum of 60 marks to get an average of atleast 65 marks.

According to the question 30<C<35

Since  C=59(F−32), we get 

30<59(F−32)<35⇒30.95<(F−32)<35.95⇒54<(F−32)<63⇒54+32<(F−32)+32<63+32⇒86<F<95

Hence  the range of temperature in degree Fahrenheit is between 86∘F and 95∘F

Let the shortest side of a triangle be x cm.Then the length of the longest side is3x cm and the length of the third side is (3x-2) cm.

Given the perimeter of the triangles at least 61cm

⇒x+3x+(3x−2)≥61⇒7x−2≥61⇒7x≥63⇒x≥9

Hence the minimum length of the shortest side = 9 cm

Given 0 > -7

Multiplying throughout by -1,we get0 < 7  [ When both sides of an inequality are multiplied by a negative number ,then the sign of inequality is reversed]

3 − 2x ≤ 9

⇒−2x≤9−3⇒−2x≤6⇒−x≤3⇒x≥−3

Since x is an integer the solution set 

Since x is an integer the solution set =

Hence the integer values which satisfy both the inequalities are