Exercise - 2.3

Exercise - . . Represent the following inequalities in the interval notation: (i) x ≥− and x < (ii) x ≤ and x ≥− (iii) x < − or x < (iv) − x > or x − < . .

Solve x < when (i) x is a natural number, (ii) x is an integer. . Solve − x ≥ when (i) x is a real number, (ii) x is an integer, (iii) x is a natural number. .

Solve: (i) ( x − ) ≤ ( − x ) . (ii) − x < x − . . To secure A grade one must obtain an average of marks or more in subjects each of maximum marks.

If one scored , , , in first four subjects, what is the minimum mark one scored in the fifth subject to get A grade in the course? . A manufacturer has litres of a percent solution of acid. How many litres of a percent acid solution must be added to it so that the acid content in the resulting mixture will be more than percent but less than percent?

. Find all pairs of consecutive odd natural numbers both of which are larger than and their sum is less than . . A model rocket is launched from the ground.

The height h reached by the rocket after t seconds from lift off is given by h ( t ) = − t + t, ≤ t ≤ . At what time the rocket is feet above the ground? . A plumber can be paid according to the following schemes: In the first scheme he will be paid rupees plus rupees per hour, and in the second scheme he will be paid rupees per hour.

If he works x hours, then for what value of x does the first scheme give better wages? . A and B are working on similar jobs but their monthly salaries differ by more than Rs . If B earns rupees 27000 per month, then what are the possibilities of A’s salary per month?