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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In the following problem, '=' stands for '/', '+' stands for '-', 'x' stands for '=', '-' stands for '>', '>' stands for '+', '< ' stands for 'x', '/' stands for '< ' When those new symbols are substituted only one will be wrong. Identify the wrong one?

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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

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

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}\} =

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

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

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:

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

EASY

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

If $| x + 2 | > 5,$ then $x \in (- \infty,$ _____ $)$ or $(3, \infty)$ .

EASY

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

By solving inequality 3(a - 6) < 4 + a, answer will be

EASY

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

By solving inequality 6x - 7 > 5, answer will be

EASY

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

If a < b and b < 0 then

EASY

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

If $- \frac{3}{4} x \leq - 3,$ then $x \geq$ _____.

EASY

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

The solution set of the inequality

3 x \leq 10, x \in N

is _____.

[\{1, 2, 3\} / \{1, 2\}]

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

1 .

P(d)R

2 .

Q(b)Z

EASY

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

If $p > 0$ and $q < 0$ then $p - q$ _____ $p$ .

In the following problem, '=' stands for '/', '+' stands for '-', 'x' stands for '=', '-' stands for '>', '>' stands for '+', '< ' stands for 'x', '/' stands for '< ' When those new symbols are substituted only one will be wrong. Identify the wrong one?

Important Questions on Linear Inequalities

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