Solve | 3 x - 7 | > 4 , x ∈ R

Given 3 x - 7 > 4 , x ∈ R if x > a then - a > x > a ⇒ - 4 > 3 x - 7 > 4 Add 7 throughout the inequality ⇒ 7 - 4 > 3 x - 7 + 7 > 4 + 7 ⇒ 3 > 3 x > 11 Divide throughout by 3 ⇒ 1 > x > 11 3 and given x ∈ R Hence, the solution set is x ∈ R : x > 11 3 ∪ x ∈ R : x < 1 .

Solve | 3 x - 7 | > 4 , x ∈ R

Given 3 x - 7 > 4 , x ∈ R if x > a then - a > x > a ⇒ - 4 > 3 x - 7 > 4 Add 7 throughout the inequality ⇒ 7 - 4 > 3 x - 7 + 7 > 4 + 7 ⇒ 3 > 3 x > 11 Divide throughout by 3 ⇒ 1 > x > 11 3 and given x ∈ R Hence, the solution set is x ∈ R : x > 11 3 ∪ x ∈ R : x < 1 .

Solve 2 ( 3 - x ) 5 < 9 5 , x ∈ R

Given 2 ( 3 - x ) 5 < 9 5 , x ∈ R if x < a then - a < x < a ⇒ - 9 5 < 2 3 - x 5 < 9 5 Multiply by 5 throughout the inequality ⇒ - 9 < 6 - 2 x < 9 Subtract throughout by 6 ⇒ - 9 - 6 < 6 - 2 x - 6 < 9 - 6 ⇒ - 15 < - 2 x < 3 Divide throughout by - 2 ⇒ 15 2 > x > - 3 2 and given x ∈ R Hence, the solution set is x ∈ R : 15 2 > x > - 3 2 .

Solve 2 x - 3 ≥ 0 graphically in a two dimensional plane.

Consider the equation 2 x - 3 = 0 ⇒ 2 x = 3 ⇒ x = 1 . 5 But, x = 1 . 5 represents a line parallel to y -axis at a distance of 1 . 5 units from it. We draw the line x = 1 . 5 , making it thick. If we put x = 0 in the given inequation, we get - 3 ≥ 0 , which is false. So, x = 0 does not satisfy the given inequation. Solution region consists of the line x = 1 . 5 and the shaded region on the right hand side of the line x = 1 . 5 , as shown below

Solve 4 x - 3 ≤ 0 graphically in a two dimensional plane.

Consider the equation 4 x - 3 = 0 ⇒ 4 x = 3 ⇒ x = 0 . 75 But, x = 0 . 75 represents a line parallel to y -axis at a distance of 0 . 75 units from it. We draw the line x = 0 . 75 , making it thick. If we put x = 0 in the given inequation, we get - 3 ≤ 0 , which is true. So, x = 0 satisfy the given inequation. Solution region consists of the line x = 0 . 75 and the shaded region on the left hand side of the line x = 0 . 75 , as shown below

E M B I B E

WBCHSE Mathematics for Class 11>Chapter 5 - Linear Inequations (In one variable)>EXERCISE 3A>Q 21

EASY

11th West Bengal Board

IMPORTANT

Earn 100

Solve $| 3 x - 7 | > 4, x \in R$

Important Questions on Linear Inequations (In one variable)

EASY

11th West Bengal Board

IMPORTANT

WBCHSE Mathematics for Class 11>Chapter 5 - Linear Inequations (In one variable)>EXERCISE 3A>Q 22

Solve $|\frac{2 (3 - x)}{5}| < \frac{9}{5}, x \in R$

EASY

11th West Bengal Board

IMPORTANT

WBCHSE Mathematics for Class 11>Chapter 5 - Linear Inequations (In one variable)>EXERCISE 3A>Q 23

The water acidity in a pool is considered normal when the average pH reading of three daily measurements is between $7.1$ and $7.8$ . If first two pH readings are $7.45$ and $7.75$ , find the range of pH value for the third reading that will result in, the acidity level being normal.

EASY

11th West Bengal Board

IMPORTANT

WBCHSE Mathematics for Class 11>Chapter 5 - Linear Inequations (In one variable)>EXERCISE 3A>Q 24

A company manufactures cassettes and its cost equation for a week is $C = 300 + 1.5 x$ and its revenue equation is $R = 2 x$ , where $x$ is the number of cassettes sold in a week. How many least number of cassettes must be sold for the company to realise a profit?

EASY

11th West Bengal Board

IMPORTANT

WBCHSE Mathematics for Class 11>Chapter 5 - Linear Inequations (In one variable)>EXERCISE 3A>Q 25

While drilling a hole in the earth, it was found that the temperature $(T ° C)$ at $x$ km below the surface of the earth was given by $T = 30 + 25 (x - 3), when 3 \leq x \leq 15$ . Between which depths will the temperature be between $200 ° C$ and $300 ° C$ ?