CENGAGE/GTEWANIMATHSSOLUTIONS

CHAPTERLINEARINEQUALITIES||ALGEBRA

DownloadDoubtnutToday

QuesNo. Question

1

CENGAGE_MATHS_ALGEBRA_LINEAR INEQUALITIES_GeneralizedMethodOfIntervals

Solve

WatchFreeVideoSolutiononDoubtnut

2

CENGAGE_MATHS_ALGEBRA_LINEAR INEQUALITIES_GeneralizedMethodOfIntervals

Solve

WatchFreeVideoSolutiononDoubtnut

3

CENGAGE_MATHS_ALGEBRA_LINEAR INEQUALITIES_GeneralizedMethodOfIntervals

Solve

WatchFreeVideoSolutiononDoubtnut

4

CENGAGE_MATHS_ALGEBRA_LINEAR INEQUALITIES_GeneralizedMethodOfIntervals

Solve

WatchFreeVideoSolutiononDoubtnut

5

CENGAGE_MATHS_ALGEBRA_LINEAR INEQUALITIES_GeneralizedMethodOfIntervals

Solve

WatchFreeVideoSolutiononDoubtnut

x2 − x − 2 > 0.

x2 − x − 1 < 0.

(x − 1)(x − 2)(1 − 2x) > 0.

(2x + 1)(x − 3)(x + 7) < 0.

< 3.2x

6

CENGAGE_MATHS_ALGEBRA_LINEAR INEQUALITIES_GeneralizedMethodOfIntervals

Solve

WatchFreeVideoSolutiononDoubtnut

7

CENGAGE_MATHS_ALGEBRA_LINEAR INEQUALITIES_GeneralizedMethodOfIntervals

Solve

WatchFreeVideoSolutiononDoubtnut

8

CENGAGE_MATHS_ALGEBRA_LINEAR INEQUALITIES_GeneralizedMethodOfIntervals

Solve

WatchFreeVideoSolutiononDoubtnut

9

CENGAGE_MATHS_ALGEBRA_LINEAR INEQUALITIES_GeneralizedMethodOfIntervals

Solve

WatchFreeVideoSolutiononDoubtnut

10

CENGAGE_MATHS_ALGEBRA_LINEAR INEQUALITIES_GeneralizedMethodOfIntervals

Solve

≥ 3.2x − 33x − 5

> .x − 2x + 2

2x − 34x − 1

x > √(1 − x).

√(x − 5) − √9 − x > 1, x ∈ Z .

− − ≥ 0.

2x2 − x + 1

1x + 1

2x− 1x3 + 1

WatchFreeVideoSolutiononDoubtnut

11

CENGAGE_MATHS_ALGEBRA_LINEAR INEQUALITIES_GeneralizedMethodOfIntervals

Solve

WatchFreeVideoSolutiononDoubtnut

12

CENGAGE_MATHS_ALGEBRA_LINEAR INEQUALITIES_GeneralizedMethodOfIntervals

Solve

WatchFreeVideoSolutiononDoubtnut

13

CENGAGE_MATHS_ALGEBRA_LINEAR INEQUALITIES_GeneralizedMethodOfIntervals

Solve

WatchFreeVideoSolutiononDoubtnut

14

CENGAGE_MATHS_ALGEBRA_LINEAR INEQUALITIES_GeneralizedMethodOfIntervals

Let beaconstant.Iftherearejust18positiveintegerssatisfyingtheinequalitythenfindthevalueof

WatchFreeVideoSolutiononDoubtnut

CENGAGE_MATHS_ALGEBRA_LINEAR INEQUALITIES_GeneralizedMethodOf

x(x + 2)2(x− 1)5(2x − 3)(x − 3)4

≥ 0.

x(2x − 1)(3x − 9)5(x − 3) < 0.

(x2 − x − 1)x2 −x−7

< −5 .

a > 2(x − a)(x − 2a)(x − a2) < 0, a.

15

Intervals

Find the set of all possible real value of a such that the inequalityholdsforall

WatchFreeVideoSolutiononDoubtnut

16

CENGAGE_MATHS_ALGEBRA_LINEAR INEQUALITIES_GeneralizedMethodOfIntervals

Findallpossiblevaluesof .

WatchFreeVideoSolutiononDoubtnut

17

CENGAGE_MATHS_ALGEBRA_LINEAR INEQUALITIES_GeneralizedMethodOfIntervals

Solve

WatchFreeVideoSolutiononDoubtnut

18

CENGAGE_MATHS_ALGEBRA_LINEAR INEQUALITIES_GeneralizedMethodOfIntervals

Solve

WatchFreeVideoSolutiononDoubtnut

19

CENGAGE_MATHS_ALGEBRA_LINEAR INEQUALITIES_GeneralizedMethodOfIntervals

Solve .

WatchFreeVideoSolutiononDoubtnut

CENGAGE_MATHS_ALGEBRA_LINEAR INEQUALITIES_GeneralizedMethodOf

(x − (a − 1))(x − (a2 + 2)) < 0 x ∈ ( − 1, 3).

x2 + 1

x2 − 2

√x − 2 ≥ − 1.

√x − 1 > √3 − x.

x + √x ≥ √x − 3

20

Intervals

Solve

WatchFreeVideoSolutiononDoubtnut

21

CENGAGE_MATHS_ALGEBRA_LINEARINEQUALITIES_AbsoluteValueOfX

If a, b, and c are nonzero rational numbers, then find the sum of all the possible

valuesof .

WatchFreeVideoSolutiononDoubtnut

22

CENGAGE_MATHS_ALGEBRA_LINEARINEQUALITIES_AbsoluteValueOfX

Solvethefollowing: (ii)

WatchFreeVideoSolutiononDoubtnut

23

CENGAGE_MATHS_ALGEBRA_LINEARINEQUALITIES_AbsoluteValueOfX

Findthevaluesof forwhichehtequation canhavefourdistinctrealsolutions.

WatchFreeVideoSolutiononDoubtnut

24

CENGAGE_MATHS_ALGEBRA_LINEARINEQUALITIES_AbsoluteValueOfX

Find the value of for which following expressions are defined: (ii)

WatchFreeVideoSolutiononDoubtnut

(x2 − 4)√x2 − 1 < 0.

+ +|a|a

|b|

b

|c|

c

|x| = 5 x2 − |x| − 2 = 0

a ||x − 2| + a| = 4

x1

√x − |x|1

√x + |x|

25

CENGAGE_MATHS_ALGEBRA_LINEARINEQUALITIES_AbsoluteValueOfX

Solvethefollowing: (ii)

WatchFreeVideoSolutiononDoubtnut

26

CENGAGE_MATHS_ALGEBRA_LINEARINEQUALITIES_AbsoluteValueOfX

Solve

WatchFreeVideoSolutiononDoubtnut

27

CENGAGE_MATHS_ALGEBRA_LINEARINEQUALITIES_AbsoluteValueOfX

Solve

WatchFreeVideoSolutiononDoubtnut

28

CENGAGE_MATHS_ALGEBRA_LINEARINEQUALITIES_AbsoluteValueOfX

Solve

WatchFreeVideoSolutiononDoubtnut

29

CENGAGE_MATHS_ALGEBRA_LINEARINEQUALITIES_AbsoluteValueOfX

Solve

WatchFreeVideoSolutiononDoubtnut

CENGAGE_MATHS_ALGEBRA_LINEARINEQUALITIES_AbsoluteValueOfX

|x − 2| = 1 2|x + 1|2 − |x + 1| = 3

1 − x = √x2 − 2x + 1.

|3x − 2| = x.

|x| = x2 − 1.

√x + 3 − 4√x − 1

+ √x + 8 − 6√x − 1 = 1

30

Provethat

WatchFreeVideoSolutiononDoubtnut

31

CENGAGE_MATHS_ALGEBRA_LINEARINEQUALITIES_AbsoluteValueOfX

For findallpossiblevaluesof (ii)

WatchFreeVideoSolutiononDoubtnut

32

CENGAGE_MATHS_ALGEBRA_LINEARINEQUALITIES_AbsoluteValueOfX

Findthepossiblevaluesof (ii) (iii)

WatchFreeVideoSolutiononDoubtnut

33

CENGAGE_MATHS_ALGEBRA_LINEARINEQUALITIES_AbsoluteValueOfX

Solve

WatchFreeVideoSolutiononDoubtnut

34

CENGAGE_MATHS_ALGEBRA_LINEARINEQUALITIES_AbsoluteValueOfX

Solve

WatchFreeVideoSolutiononDoubtnut

35

CENGAGE_MATHS_ALGEBRA_LINEARINEQUALITIES_AbsoluteValueOfX

Solve

WatchFreeVideoSolutiononDoubtnut

√x2 + 2x+ 1 −√x2 − 2x + 1

= { − 2, x < − 12x, − 1 ≤ x

≤ 12, x > 1

x ∈ R, |x − 3| − 2 4 − |2x + 3|

√|x| − 2 √3 − |x− 1| √4 −√x2

|x − 3| + |x − 2| = 1.

x2 − 4|x| + 3 < 0.

0 < |x| < 2.

36

CENGAGE_MATHS_ALGEBRA_LINEARINEQUALITIES_AbsoluteValueOfX

Solve

WatchFreeVideoSolutiononDoubtnut

37

CENGAGE_MATHS_ALGEBRA_LINEARINEQUALITIES_AbsoluteValueOfX

Solve

WatchFreeVideoSolutiononDoubtnut

38

CENGAGE_MATHS_ALGEBRA_LINEARINEQUALITIES_AbsoluteValueOfX

Solve

WatchFreeVideoSolutiononDoubtnut

39

CENGAGE_MATHS_ALGEBRA_LINEARINEQUALITIES_AbsoluteValueOfX

Solve

WatchFreeVideoSolutiononDoubtnut

40

CENGAGE_MATHS_ALGEBRA_LINEARINEQUALITIES_AbsoluteValueOfX

Solve

WatchFreeVideoSolutiononDoubtnut

41

CENGAGE_MATHS_ALGEBRA_LINEARINEQUALITIES_AbsoluteValueOfX

Solve

WatchFreeVideoSolutiononDoubtnut

|3x − 2| < 4.

1 ≤ |x − 2| ≤ 3.

0 < |x − 3| ≤ 5.

||x − 1| − 2| < 5.

|x − 3| ≥ 2.

||x| − 3| > 1.

42

CENGAGE_MATHS_ALGEBRA_LINEARINEQUALITIES_AbsoluteValueOfX

Solve

WatchFreeVideoSolutiononDoubtnut

43

CENGAGE_MATHS_ALGEBRA_LINEARINEQUALITIES_AbsoluteValueOfX

Solve

WatchFreeVideoSolutiononDoubtnut

44

CENGAGE_MATHS_ALGEBRA_LINEARINEQUALITIES_AbsoluteValueOfX

Solve

WatchFreeVideoSolutiononDoubtnut

45

CENGAGE_MATHS_ALGEBRA_LINEARINEQUALITIES_AbsoluteValueOfX

Solve

WatchFreeVideoSolutiononDoubtnut

46

CENGAGE_MATHS_ALGEBRA_LINEARINEQUALITIES_AbsoluteValueOfX

Solve

WatchFreeVideoSolutiononDoubtnut

47

CENGAGE_MATHS_ALGEBRA_LINEARINEQUALITIES_AbsoluteValueOfX

If

,theninwhichquadrantdoes lies?

|x − 1| + |x − 2| ≥ 4.

|x + 1| + |2x− 3| = 4.

|x| + |x − 2| = 2.

|2x − 3| + |x− 1| = |x− 2|.

∣∣x2 + x − 4∣∣ = ∣∣x2 − 4∣∣ + |x|.

|sin x + cos x| = |sinx|

+ |cos x|(sin x, cosx ≠ 0)x

WatchFreeVideoSolutiononDoubtnut

48

CENGAGE_MATHS_ALGEBRA_LINEARINEQUALITIES_AbsoluteValueOfX

Is true for any If it is true, then find thevaluesof

WatchFreeVideoSolutiononDoubtnut

49

CENGAGE_MATHS_ALGEBRA_LINEARINEQUALITIES_AbsoluteValueOfX

Solve

WatchFreeVideoSolutiononDoubtnut

50

CENGAGE_MATHS_ALGEBRA_LINEARINEQUALITIES_AbsoluteValueOfX

Solve

WatchFreeVideoSolutiononDoubtnut

|tanx + cotx| < |tanx| + |cotx| x?x.

∣∣∣∣∣∣ ≤ 1.

x − 3x + 1

∣∣∣∣∣∣ + |x + 1| = .

x + 1x

(x + 1)2

|x|

51

CENGAGE_MATHS_ALGEBRA_LINEARINEQUALITIES_AbsoluteValueOfX

Solve

WatchFreeVideoSolutiononDoubtnut

52

CENGAGE_MATHS_ALGEBRA_LINEARINEQUALITIES_AbsoluteValueOfX

Solve

WatchFreeVideoSolutiononDoubtnut

53

CENGAGE_MATHS_ALGEBRA_LINEARINEQUALITIES_AbsoluteValueOfX

Solve

WatchFreeVideoSolutiononDoubtnut

54

CENGAGE_MATHS_ALGEBRA_LINEARINEQUALITIES_AbsoluteValueOfX

Solve

WatchFreeVideoSolutiononDoubtnut

∣∣∣1 +∣∣∣ > 2

3x

∣∣x2 − 2x∣∣ + |x − 4| > ∣∣x2 − 3x + 4∣∣.

|2x − 1| + |4 − 2x| < 3.

≤x

x + 21|x|

55

CENGAGE_MATHS_ALGEBRA_LINEARINEQUALITIES_AbsoluteValueOfX

Solve

WatchFreeVideoSolutiononDoubtnut

56

CENGAGE_MATHS_ALGEBRA_LINEARINEQUALITIES_Inequalities

Findallintegers forwhich

WatchFreeVideoSolutiononDoubtnut

57

CENGAGE_MATHS_ALGEBRA_LINEARINEQUALITIES_Functions

If

find

WatchFreeVideoSolutiononDoubtnut

58

CENGAGE_MATHS_ALGEBRA_LINEARINEQUALITIES_Inequalities

Let . Find all the real values of for which takes real

values.

WatchFreeVideoSolutiononDoubtnut

59

CENGAGE_MATHS_ALGEBRA_LINEARINEQUALITIES_Inequalities

Findallrealvaluesof whichsatisfy

WatchFreeVideoSolutiononDoubtnut

( ) > 9.13

|x+ 2 |

2− |x |

x (5x − 1) < (x + 1)2 < (7x − 3).

f(x) = x9 − 6x8 − 2x7 + 12x6 + x4

− 7x3 + 6x2 + x − 3,f(6).

y = √ (x + 1)(x − 3)

(x − 2)x y

xx2 − 3x+ 2 > 0andx2 − 2x − 4 ≤ 0.

60

CENGAGE_MATHS_ALGEBRA_LINEARINEQUALITIES_Inequalities

Findthesetofall foirwhich

WatchFreeVideoSolutiononDoubtnut

61

CENGAGE_MATHS_ALGEBRA_LINEARINEQUALITIES_AbsoluteValueOfX

Solve

WatchFreeVideoSolutiononDoubtnut

62

CENGAGE_MATHS_ALGEBRA_LINEARINEQUALITIES_AbsoluteValueOfX

Thesumofrealrootsoftheequation a.4b.1c.2d.2

WatchFreeVideoSolutiononDoubtnut

63

CENGAGE_MATHS_ALGEBRA_LINEARINEQUALITIES_Inequalities

Thelargestintervalforwhich

WatchFreeVideoSolutiononDoubtnut

64

CENGAGE_MATHS_ALGEBRA_LINEARINEQUALITIES_AbsoluteValueOfX

If satifies then (a) (b).(c). (d).Noneofthese

WatchFreeVideoSolutiononDoubtnut

CENGAGE_MATHS_ALGEBRA_LINEARINEQUALITIES_AbsoluteValueOfX

Thesetofallrealnumbers forwhich is b.

x > .2x

(2x2 + 5x + 2)1

(x + 1)

∣∣x2 + 4x + 3∣∣ + 2x + 5 = 0.

|x − 2|2 + |x − 2| − 2 = 0is

x12 − x9 + x4 − x + 1 > 0

x |x − 1| + |x− 2| + |x − 3| ≥ 6, 0 ≤ x ≤ 4x ≤ − 2 or ≥ 4 x ≤ 0 or x ≥ 4

x x2 − |x + 2| + x > 0 ( − ∞, − 2)

65 c. d.

WatchFreeVideoSolutiononDoubtnut

66

CENGAGE_MATHS_ALGEBRA_LINEARINEQUALITIES_Intervals

IfSisthesetofallreal suchthat ispositive b.

c. d. e.Noneofthese

WatchFreeVideoSolutiononDoubtnut

DownloadDoubtnuttoAskAnyMathQuestionByjustaclick

GetAVideoSolutionForFreeinSeconds

DoubtnutHasMoreThan1LakhVideoSolutions

Free Video Solutions of NCERT, RD Sharma, RS Aggarwal, Cengage(G.Tewani), Resonance DPP, Allen, Bansal, FIITJEE, Akash, Narayana,VidyaMandir

DownloadDoubtnutToday

( −∞, − √2) ∪ (√2, ∞) ( − ∞, − 1) ∪ (1, ∞) (√2,∞)

x2x − 1

2x3 + 3x2 + x(− ∞, − )3

2

( − , )3214

( − , )1412

( , 3)12

https://doubtnut.app.link/Brs4q69ExQ