x ∈ ℝ : 6 + x - x 2 2 x + 5 ≥ 6 + x - x 2 x + 4 =

( - ∞ , - 4 ] ∪ - 5 2 , - 1

( - ∞ , - 4 ] ∪ [ - 2 , - 1 ]

If x + 5 ≥ 10 , then

x ∈ ( - ∞ , - 15 ] ∪ [ 5 , ∞ )

x ∈ - ∞ , - 15 ∪ [ 5 , ∞ )

HARD

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If 33 + 44 = 24, 44 + 66 = 48, then 55 + 77 = ?

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Important Questions on Linear Inequalities

MEDIUM

Mathematics>Algebra>Linear Inequalities>Solutions of Linear Inequalities in One Variable

Let

[x]

be the greatest integer less than or equal to

x

, for a real number

x

. Then the equation

[x^{2}] = x + 1

has

MEDIUM

Mathematics>Algebra>Linear Inequalities>Solutions of Linear Inequalities in One Variable

The set of real values of

x

for which the inequality

|x - 1| + |x + 1| < 4

always holds good is

HARD

Mathematics>Algebra>Linear Inequalities>Solutions of Linear Inequalities in One Variable

The equation

| x | + |\frac{x}{x - 1}| = \frac{x^{2}}{| x - 1 |}

will be always true for

x

, belonging to

HARD

Mathematics>Algebra>Linear Inequalities>Solutions of Linear Inequalities in One Variable

\frac{6 x^{2} - 5 x - 3}{x^{2} - 2 x + 6} \leq 4,

then the least and the highest values of

4 x^{2}

are

MEDIUM

Mathematics>Algebra>Linear Inequalities>Solutions of Linear Inequalities in One Variable

Two equations are given, you have to solve the both the equations:

$(i) X^{2} = 196$

$(i i) Y^{2} + 2 y - 48 = 0$

MEDIUM

Mathematics>Algebra>Linear Inequalities>Solutions of Linear Inequalities in One Variable

Let

x = [\frac{a + 2 b}{a + b}]

and

y = \frac{a}{b}

, where

a

and

b

are positive integers. If

y^{2} > 2

, then

HARD

Mathematics>Algebra>Linear Inequalities>Solutions of Linear Inequalities in One Variable

\{x \in ℝ : \frac{\sqrt{6 + x - x^{2}}}{2 x + 5} \geq \frac{\sqrt{6 + x - x^{2}}}{x + 4}\} =

MEDIUM

Mathematics>Algebra>Linear Inequalities>Solutions of Linear Inequalities in One Variable

The maximum value of

2 x + y

subject to

3 x + 5 y \leq 26

and

5 x + 3 y \leq 30, x \geq 0, y \geq 0

is:

EASY

Mathematics>Algebra>Linear Inequalities>Solutions of Linear Inequalities in One Variable

|x + 5| \geq 10

, then

MEDIUM

Mathematics>Algebra>Linear Inequalities>Solutions of Linear Inequalities in One Variable

Which of the following statement(s) is/are true?

I. $(7)^{450} > (9)^{300}$

II . ${(2)}^{900} > {(7)}^{450}$

MEDIUM

Mathematics>Algebra>Linear Inequalities>Solutions of Linear Inequalities in One Variable

The number of non-negative integer solutions of the equations

6 x + 4 y + z = 200

and

x + y + z = 100

MEDIUM

Mathematics>Algebra>Linear Inequalities>Solutions of Linear Inequalities in One Variable

Directions: In the following questions the symbols (a), (b), (c), (d) and (e) have been used having their meanings as-
A (a) B means A is smaller than B.
A (b) B means A is greater or equal to B.
A (c) B means A is greater than B.
A (d) B means A is equal to B.
A (e) B means A is shorter or equal to B.
Assuming the statement given in each of the question as true deduce which of the two inferences I and II is/are true ?

Statement: N (a) L, L (d) P, P (e) H
Inference: I. L (e) H II. H (c) N

EASY

Mathematics>Algebra>Linear Inequalities>Solutions of Linear Inequalities in One Variable

In the following questions, the symbols @, §,*, # and & used with the following meaning as illustrated below:

P § Q means P is not smaller than Q
P @ Q means P is neither smaller than nor equal to Q
P # Q means P is neither greater than nor equal to Q
P & Q means P is neither greater than nor smaller than Q
P * Q means P is not greater than Q

Now, in each of the following questions assuming the given statements to be true, find which of the four conclusions I, II, III and IV given below them is/are definitely true and give your answer accordingly.

Statements: M § K, K @ N, N * R, R # W
Conclusions: I. W @ K
II. M§ R
III. K @ W
IV. M @ N

EASY

Mathematics>Algebra>Linear Inequalities>Solutions of Linear Inequalities in One Variable

In the following questions, the symbols @, !, *, # and & used with the following meaning as illustrated below:

P ! Q means P is not smaller than Q
P @ Q means P is neither smaller than nor equal to Q
P # Q means P is neither greater than nor equal to Q
P & Q means P is neither greater than nor smaller than Q
P * Q means P is not greater than Q

Now, in each of the following questions assuming the given statements to be true, find which of the four conclusions I, II, III and IV given below them is/are definitely true and give your answer accordingly.

Statements: D # R, R * K, K @ F, F ! J
Conclusions: I. J # R
II. J # K
III. R # F
IV. K @ D

EASY

Mathematics>Algebra>Linear Inequalities>Solutions of Linear Inequalities in One Variable

In the following questions, the symbols @, !, *, # and & used with the following meaning as illustrated below:

P ! Q means P is not smaller than Q
P @ Q means P is neither smaller than nor equal to Q
P # Q means P is neither greater than nor equal to Q
P & Q means P is neither greater than nor smaller than Q
P * Q means P is not greater than Q

Now, in each of the following questions assuming the given statements to be true, find which of the four conclusions I, II, III and IV given below them is/are definitely true and give your answer accordingly.

Statements: H @ T, T # F, F& E, E * V
Conclusions:
I. V ! F
II. E @ T
III. H @ V
IV. T # V

MEDIUM

Mathematics>Algebra>Linear Inequalities>Solutions of Linear Inequalities in One Variable

In the following question, the signs (a), (b), =, (c) and (d) are being used which have the following meanings :
A (a) B means A is smaller than B.
A (b) B means A is smaller or equal to B.
A = B means A is equal to B.
A (c) B means A is greater than B.
A (d) B means A is greater or equal to B.
Assuming the statement given in each of the following questions deduce which of the two inferences I and II is/are true ?

Statement- K (c) L, L (b) R, R = P
Inference-
I. P(d)L
II. K(c)R

EASY

Mathematics>Algebra>Linear Inequalities>Solutions of Linear Inequalities in One Variable

In each of the following questions, assuming the given statements to be true, find which of the two conclusions I and II given below is/are definitely true. Give answer 1. If only conclusion I is true. 2. If only conclusion II is true. 3. If either conclusion I or II is true. 4. If neither conclusion I nor II is true. 5. If both conclusions I and II are true.

Statements : P > Q, Q < E, E > F, F> G, G > H, H > I
Conclusions: I. E > I II. E < I

EASY

Mathematics>Algebra>Linear Inequalities>Solutions of Linear Inequalities in One Variable

In the following questions, the symbols @, ©, &, % and # are used with the following meaning as illustrated below:

'P & Q' means 'P is not greater than Q'.
'P@Q' means 'P is neither smaller than nor equal to Q'.
'P # Q' means' P is not smaller than Q'.
'P © Q' means 'P is neither greater than nor equal to Q'.
'P % Q' means 'P is neither smaller than nor greater than Q'.
Now in each of the following questions assuming the given statements to be true, find which of the two conclusions $1$ and $2$ given below them is/are definitely true and give your answer accordingly.

Statements: x © d, m & x, n @ m , c#m
Conclusions:

$1 .$ c@d $2 .$ d#c

EASY

Mathematics>Algebra>Linear Inequalities>Solutions of Linear Inequalities in One Variable

In the following questions, the symbols @, ©, &, % and # are used with the following meaning as illustrated below:

'P & Q' means 'P is not greater than Q'.
'P@Q' means 'P is neither smaller than nor equal to Q'.
'P # Q' means' P is not smaller than Q'.
'P © Q' means 'P is neither greater than nor equal to Q'.
'P % Q' means 'P is neither smaller than nor greater than Q'.
Now in each of the following questions assuming the given statements to be true, find which of the two conclusions I and II given below them is/are definitely true and give your answer accordingly.

Statements: s%e, z# o, o@t, e@t
Conclusions:

$I$ . e@o

$II$ . t@z

EASY

Mathematics>Algebra>Linear Inequalities>Solutions of Linear Inequalities in One Variable

In the following question the symbols #, *, @, ! and = are used with the following meanings:
A # B means A is greater than B.
A * B means A is greater than or equal to B.
A @ B means A is equal to B.
A ! B means A is lesser than B.
A = B means A is lesser than or equal to B.
Now in each of the following questions, assuming the three statements to be true, find which of the two conclusions I and II given below them is/are true.

Give answer:
1) if only conclusion I is true
2) if only conclusion II is true
3) if either conclusion I or conclusion II is true
4) if neither conclusion I nor conclusion II is true
5) if both conclusions I and II are true.

Statements: P # Q, R ! P, R * Q
Conclusions:
I. Q @ R
II. Q ! R

If 33 + 44 = 24, 44 + 66 = 48, then 55 + 77 = ?

Important Questions on Linear Inequalities

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