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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: (3x-4)/2 >= (x+1)/4 -1Answer: Q 2: 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 lie between 10 and 19Odd number must be greater than 19Odd number must be lesser than 10 Q 3: 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.11 cm 15 cm9 cm Q 4: x/2 < = (5x-2)/3 - (7x-3)/5Answer: Q 5: 5x-3 > = 3x-5Answer: Q 6: 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?404535 Q 7: IQ of a person is given by the formula IQ = MA/CA * 100 where MA is mental age and CA is chronical age. If 80 <= IQ <= 140 for a group of 12 year children, find the range of their mental age.More than 16.8Less than 9.6Atleast 9.6 but not more than 16.8 Q 8: A solution of 8% boric acid is to be diluted by adding a 2% boric acid to it. The resulting mixture is to be more than 4%but less than 6% boric acid . If we have 640 litres of the 8% solution, how many litres of the 2% solution will have to be added?less than 3 20 litresmore than 320 litres but less than 1280 litresmore than 1280 litres Question 9: This question is available to subscribers only! Question 10: This question is available to subscribers only!

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