Forum

Linear Inequalities

To receive Grade ‘A’ in a course, one must obtain an average of 90 marks or
more in five examinations (each of 100 marks). If Sunita’s marks in first four
examinations are 87, 92, 94 and 95, find minimum marks that Sunita must obtain
in fifth examination to get grade ‘A’ in the course

Linear Inequalities

Ravi obtained 70 and 75 marks in first two unit test. Find the minimum marks he
should get in the third test to have an average of at least 60 marks

Linear Inequalities

Solve the inequalities and show the graph of the solution in each
case on number line

17. 3x – 2 < 2x + 1 18. 5x – 3 > 3x – 5
19. 3 (1 – x) < 2 (x + 4) 20. (5 – 2) (7 –3) – 2 3 5

Linear Inequalities

Solve the inequalities for real x
13. 2 (2x + 3) – 10 < 6 (x – 2) 14. 37 – (3x + 5) > 9x – 8 (x – 3)
15.
(5 2) (7 3)
4 3 5
x x x − −
< − 16. (2 1) (3 2) (2 ) 3 4 5

Linear Inequalities

Solve the inequalities for real x
5. 4x + 3 < 5x + 7 6. 3x – 7 > 5x – 1
7. 3(x – 1) ≤ 2 (x – 3) 8. 3 (2 – x) ≥ 2 (1 – x)
9. 11
2 3
x x
x + + < 10. 1 3 2 x x > +
11.
3( 2) 5(2 )
5 3
x − − x
≤ 12.
1 3 1 4 ( 6)
2 5 3
x
x
    + ≥ −

Linear Inequalities

Solve 3x + 8 >2, when
(i) x is an integer. (ii) x is a real number.

Linear Inequalities

Solve 5x – 3 < 7, when (i) x is an integer. (ii) x is a real number

Linear Inequalities

Solve – 12x > 30, when
(i) x is a natural number. (ii) x is an integer

Linear Inequalities

Solve 24x < 100, when (i) x is a natural number. (ii) x is an integer

Linear Inequalities

Find all pairs of consecutive odd natural numbers, both of which are larger
than 10, such that their sum is less than 40