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### High School Mathematics - 27.11 Graphical Representation of Solutions of Inequalities

 Example 1: Solve 7x+3 < 5x+9 Solution: We have 7x+3 < 5x+9 2x < 6 or x < 3 Example 2: The marks obtained by a student in his exams are 62 and 48. What marks should he get in his next test to get an average of 60? Solution: (62+8+x)/3 > = 60 x > = 70 Answer: The student must obtain a minimum of 70 marks to get an average of 60.
 Q 1: The marks obtained by a student in two tests were 70 and 75, what should he score in his third test to get an average of 60?403545 Q 2: 37 - (3x+5) >= 9x-8(x-3)Answer: Q 3: (3x-4)/2 >= (x+1)/4 -1Answer: Q 4: A manufacturer has 6000 litres of a 12% solution of acid. How many litres of 30% acid solution must be added to it so that the acid content in the resulting mixture will be more than 15% but less than 18%?120>x<300120120>x>300 Q 5: The longest side is of a triangle is 3 times the shortest side and third side is 2cm shorter than the longest side. If the perimeter of the triangle is atleast 61 cm, find the minimum length of the shortest side.9 cm 15 cm11 cm Q 6: 5x-3 > = 3x-5Answer: Q 7: Find all pairs of consecutive odd natural numbers, both of which are larger than 10, such that their sum is less than 40.Odd number must be lesser than 10Odd number must lie between 10 and 19Odd number must be greater than 19 Q 8: x/2 < = (5x-2)/3 - (7x-3)/5Answer: Question 9: This question is available to subscribers only! Question 10: This question is available to subscribers only!