If x + 5 ≥ 10 , then

x ∈ ( - ∞ , - 15 ] ∪ [ 5 , ∞ )

x ∈ - ∞ , - 15 ∪ [ 5 , ∞ )

Solve the following inequation and write down the solution set 11 x - 4 < 15 x + 4 ≤ 13 x + 14 , x ∈ W . Represent the solution on a real number line.

Given: 11 x - 4 < 15 x + 4 ≤ 13 x + 14 , x ∈ W Consider, 11 x - 4 < 15 x + 4 ⇒ 11 x - 4 - 4 < 15 x + 4 - 4 [subtract 4 from both sides] ⇒ 11 x - 8 < 15 x ⇒ 11 x - 8 - 11 x < 15 x - 11 x [subtract 11 x from both sides] ⇒ - 8 < 4 x ⇒ - 8 4 < 4 x 4 [divide both sides by 4 ] ⇒ x > - 2 . . . . . . . i Now, consider, 15 x + 4 ≤ 13 x + 14 ⇒ 15 x + 4 - 13 x ≤ 13 x + 4 - 13 x [subtract 13 x from both sides] ⇒ 2 x + 4 ≤ 14 ⇒ 2 x + 4 - 4 ≤ 14 - 4 [ subtract 4 from both sides] ⇒ 2 x ≤ 10 ⇒ 2 x 2 ≤ 10 2 [divide both sides by 5 ] ⇒ x ≤ 5 . . . . . . i i ∴ From equations i and i i , we get: - 2 < x ≤ 5 Since, x ∈ W . ∴ Solution set = 0 , 1 , 2 , 3 , 4 , 5 On the number line it can be represented as

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Largest integral value of $x$ satisfying $\frac{x^{2} + 2 x - 4}{x^{2} - 4 x + 5} > 3$ is

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Important Questions on Linear Inequalities

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

What is the greatest integer not exceeding the sum

\sum_{n = 1}^{1599} \frac{1}{\sqrt{n}} ?

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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

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

|x + 5| \geq 10

, then

EASY

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

Solve the following inequation and write down the solution set $11 x - 4 < 15 x + 4 \leq 13 x + 14, x \in W$ .

Represent the solution on a real number line.

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

The maximum value of

z = 7 x + 5 y

subject to

2 x + y \leq 100, 4 x + 3 y \leq 240, x \geq 0, y \geq 0

HARD

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

Solve the following inequality, write down the solution set and represent it on the real number line:

$- 2 + 10 x \leq 13 x + 10 < 24 + 10 x, x \in Z$

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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

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

2 \leq 3 x - 4 \leq 5, x \in R

, then

x

belongs to the interval

HARD

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

The solution set of the rational inequality

\frac{x + 9}{x - 6} \leq 0

EASY

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

The smallest prime number satisfying the inequality

\frac{2 n - 3}{3} \geq \frac{n - 1}{6} + 1

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

Solve the following inequation and represent the solution set on the number line.

$\frac{3 x}{5} + 2 < x + 4 \leq \frac{x}{2} + 5, x \in R$

EASY

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

The speed of a boat in still water and the speed of the current is in ratio $5 : 1$ . If the difference between distances covered by the boat in going $2 hours$ upstream and $2 hours$ downstream is $8 km$ .

I. Quantity I - Speed of boat in still water

II. Quantity II -A cyclist goes $30 km$ in $3 hours$

Find the relation between these two quantities.

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

The solution set of

|x - 1| \geq |x - 3|

is -

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

x \in R

and

0 \leq (3 x - 5) / 2 \leq 8,

then the minimum and maximum values of

' x'

are

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

Solve the inequality

3 (1 - x) < 2 (x + 4)

and draw this solution on the number line.

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

The solution set of the inequality

- 2 \leq \frac{3 x + 2}{2} < 7

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

x^{2} - 6 x - 27 > 0

, then which one of the following is correct?

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

For all

n \in ℕ, n \in ℕ,

, if

1^{2} + 2^{2} + 3^{2} + \dots + n^{2} > x

, then

x =

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

The number of integers satisfying the inequality

|n^{2} - 100| < 50

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

The least positive integer

n

for which

\sqrt{n + 1} - \sqrt{n - 1} < 0.2

Largest integral value of x satisfying x2+2x-4x2-4x+5>3 is

Important Questions on Linear Inequalities

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Largest integral value of $x$ satisfying $\frac{x^{2} + 2 x - 4}{x^{2} - 4 x + 5} > 3$ is