The greatest integer which is such that if 7 is added to its double

Find the greatest integer which is such that if 7 is added to its double, the resulting number becomes greater than three times the integer.

Solution:

Let the greatest integer = x
According to the condition,
2x + 7 > 3x
⇒ 2x – 3x > – 7
⇒ – x > – 7
⇒ x < 7
Value of x which is greatest = 6 Ans.

One-third of a bamboo pole is buried in mud, one-sixth of it is in water and the part above the water is greater than or equal to 3 metres. Find the length of the shortest pole.

Solution:

Let the length of the shortest pole = x metre
Length of pole which is burried in mud = \\ \frac { x }{ 3 }
Length of pole which is in the water = \\ \frac { x }{ 6 }
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 4 Linear Inequations Ex 4 Q42.1

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