Solve: - 3 ≤ 4 - 7 x 2 ≤ 18

According to question Given that - 3 ≤ 4 - 7 x 2 ≤ 18 Substracting each side by 4 ⇒ - 3 - 4 ≤ 4 - 7 x 2 - 4 ≤ 18 - 4 ⇒ - 7 ≤ - 7 x 2 ≤ 14 ⇒ - 14 ≤ - 7 x ≤ 28 Dividing each side by - 7 ⇒ - 4 ≤ x ≤ 2 Hence interval for x is - 4 , 2

Solve: 3 ( 2 - x ) ≥ 2 ( 1 - x )

Given that, 3 ( 2 - x ) ≥ 2 ( 1 - x ) ⇒ 6 - 3 x ⩾ 2 - 2 x ⇒ - 3 x + 2 x ≥ 2 - 6 ⇒ - x ≥ - 4 Multiplying both sides by - 1 , we get, x ≤ 4 Hence, x ∈ ( - ∞ , 4 ]

Solve: 5 x - 6 x + 6 < 1

Given that, 5 x - 6 x + 6 < 1 ⇒ 5 x - 6 x + 6 - 1 < 0 ⇒ 5 x - 6 - x - 6 x + 6 < 0 ⇒ 4 x - 12 x + 6 < 0 ⇒ 4 x - 3 x + 6 < 0 ⇒ x - 3 x + 6 < 0 From here we have two cases Case (i): x - 3 < 0 and x + 6 > 0 ⇒ x < 3 and x > - 6 ⇒ x ∈ - 6 , 3 Case (ii): x - 3 > 0 and x + 6 < 0 ⇒ x > 3 and x < - 6 Which is not possible as their intersection is an empty set. Hence, the solution of the given inequality is - 6 , 3

Solve: 2 x - 1 3 ≥ 3 x - 2 4 - 2 - x 5 , x ∈ R

Given that, 2 x - 1 3 ≥ 3 x - 2 4 - 2 - x 5 ⇒ 2 x - 1 3 ≥ 5 ( 3 x - 2 ) - 4 ( 2 - x ) 20 ⇒ 2 x - 1 3 ≥ 15 x - 10 - 8 + 4 x 20 ⇒ 2 x - 1 3 ⩾ 19 x - 18 20 ⇒ 40 x - 20 ⩾ 57 x - 54 ⇒ 40 x - 57 x ≥ - 54 + 20 - 17 x ⩾ - 34 Dividing both side by - 17 , we get, x ≤ 2 Hence, x ∈ ( - ∞ , 2 ]

E M B I B E

Golden MATHEMATICS CLASS 11>Chapter 6 - Linear Inequalities>OBJECTIVE TYPE QUESTIONS>Q 10

EASY

11th CBSE

IMPORTANT

Earn 100

The region represented by a system of inequations $x \geq 0, y \geq 0$ is in

42.86% studentsanswered this correctly

Important Questions on Linear Inequalities

EASY

11th CBSE

IMPORTANT

Golden MATHEMATICS CLASS 11>Chapter 6 - Linear Inequalities>SELF EVALUATION TEST>Q 1

Solve

24 x < 100

, if

x

is a natural number, then find the number of solutions.

EASY

11th CBSE

IMPORTANT

Golden MATHEMATICS CLASS 11>Chapter 6 - Linear Inequalities>SELF EVALUATION TEST>Q 2

Solve:

4 x + 3 < 6 x + 7

EASY

11th CBSE

IMPORTANT

Golden MATHEMATICS CLASS 11>Chapter 6 - Linear Inequalities>SELF EVALUATION TEST>Q 3

If the solution set of inequality

3 (\frac{x - 2}{5}) \geq 5 (\frac{2 - x}{3})

is

x \in [a, \infty), \forall a \in R

, then the value of

a

is

EASY

11th CBSE

IMPORTANT

Golden MATHEMATICS CLASS 11>Chapter 6 - Linear Inequalities>SELF EVALUATION TEST>Q 4

Solve:

- 3 \leq 4 - \frac{7 x}{2} \leq 18

EASY

11th CBSE

IMPORTANT

Golden MATHEMATICS CLASS 11>Chapter 6 - Linear Inequalities>SELF EVALUATION TEST>Q 5

Solve:

3 (2 - x) \geq 2 (1 - x)

EASY

11th CBSE

IMPORTANT

Golden MATHEMATICS CLASS 11>Chapter 6 - Linear Inequalities>SELF EVALUATION TEST>Q 6

Solve: $\frac{5 x - 6}{x + 6} < 1$

EASY

11th CBSE

IMPORTANT

Golden MATHEMATICS CLASS 11>Chapter 6 - Linear Inequalities>SELF EVALUATION TEST>Q 7

Solve:

\frac{2 x - 1}{3} \geq \frac{3 x - 2}{4} - \frac{2 - x}{5}, x \in R

MEDIUM

11th CBSE

IMPORTANT

Golden MATHEMATICS CLASS 11>Chapter 6 - Linear Inequalities>SELF EVALUATION TEST>Q 8

A man wants to cut three lengths from a single piece of board of length

91

cm. The second length is to be

3

cm longer than the shortest and the third length is to be twice as long as the shortest. What are the possible lengths of the shortest board if the third piece is to be at least