Solve 1 ≥ 15 - 7 x > 2 x - 27 , x ∈ N .

Given inequation is 1 ≥ 15 - 7 x > 2 x - 27 Given equation has two parts 1 ≥ 15 - 7 x and 15 - 7 x > 2 x - 27 Solve both the equation simultaneously 1 ≥ 15 - 7 x and 15 - 7 x > 2 x - 27 1 - 15 ≥ - 7 x and - 7 x - 2 x > - 27 - 15 - 14 ≥ - 7 x and - 9 x > - 42 2 ≤ x and x < 14 3 ⇒ 2 ≤ x < 14 3 But, x ∈ N Thus, the solution set is 2 , 3 , 4

Solve 4 x - 10 3 ≤ 5 x - 7 2 , x ∈ R and represent the solution set on the number line.

Given 4 x - 10 3 ≤ 5 x - 7 2 Cross-multiplying 2 4 x - 10 ≤ 3 5 x - 7 8 x - 20 ≤ 15 x - 21 8 x - 15 x ≤ - 21 + 20 - 7 x ≤ - 1 On multiplying - 1 both side sign will reverse 7 x ≥ 1 x ≥ 1 7 Since x ∈ R Thus, the solution set is x : x ∈ R , x ≥ 1 7 .

Solve 3 x 5 - 2 x - 1 3 > 1 , x ∈ R and represent the solution set on the number line.

Given 3 x 5 - 2 x - 1 3 > 1 Taking LCM and cross-multiplying : 3 x × 3 15 - 5 2 x - 1 15 > 1 9 x - 10 x + 5 15 > 1 9 x - 10 x + 5 > 15 - x > 10 On multiplying - 1 both the side sign will reverse x < - 10 But x ∈ R , so the solution set is { x : x ∈ R , x < - 10 } . The graphical representation is :

E M B I B E

Understanding ICSE Mathematics Class 10>Algebra>Chapter 4 - Linear Inequations>Exercise 4

M L Aggarwal Solutions for Exercise 1: Exercise 4

Author:M L Aggarwal

M L Aggarwal Mathematics Solutions for Exercise - M L Aggarwal Solutions for Exercise 1: Exercise 4

Attempt the practice questions from Exercise 1: Exercise 4 with hints and solutions to strengthen your understanding. Understanding ICSE Mathematics Class 10 solutions are prepared by Experienced Embibe Experts.

Questions from M L Aggarwal Solutions for Exercise 1: Exercise 4 with Hints & Solutions

EASY

10th ICSE

IMPORTANT

Understanding ICSE Mathematics Class 10>Chapter 4 - Linear Inequations>Exercise 4>Q 15

Solve $1 \geq 15 - 7 x > 2 x - 27, x \in N$ .

EASY

10th ICSE

IMPORTANT

Understanding ICSE Mathematics Class 10>Chapter 4 - Linear Inequations>Exercise 4>Q 17

Solve $\frac{4 x - 10}{3} \leq \frac{5 x - 7}{2}, x \in R$ and represent the solution set on the number line.

MEDIUM

10th ICSE

IMPORTANT

Understanding ICSE Mathematics Class 10>Chapter 4 - Linear Inequations>Exercise 4>Q 18

Solve $\frac{3 x}{5} - \frac{2 x - 1}{3} > 1, x \in R$ and represent the solution set on the number line.

EASY

10th ICSE

IMPORTANT

Understanding ICSE Mathematics Class 10>Chapter 4 - Linear Inequations>Exercise 4>Q 19

Given that $x \in R$ , solve the following inequation and graph the solution on the number line: $- 1 \leq 3 + 4 x < 23$ .

HARD

10th ICSE

IMPORTANT

Understanding ICSE Mathematics Class 10>Chapter 4 - Linear Inequations>Exercise 4>Q 30

Given $20 - 5 x < 5 (x + 8),$ find the smallest value of $x$ when: $x \in I$ .

HARD

10th ICSE

IMPORTANT

Understanding ICSE Mathematics Class 10>Chapter 4 - Linear Inequations>Exercise 4>Q 30

Given $20 - 5 x < 5 (x + 8),$ find the smallest value of $x$ when: $x \in W$ .

EASY

10th ICSE

IMPORTANT

Understanding ICSE Mathematics Class 10>Chapter 4 - Linear Inequations>Exercise 4>Q 30

Given $20 - 5 x < 5 (x + 8),$ find the smallest value of $x$ when $x \in N$ .

HARD

10th ICSE

IMPORTANT

Understanding ICSE Mathematics Class 10>Chapter 4 - Linear Inequations>Exercise 4>Q 35

One-third of a bamboo pole is buried in mud, one-sixth of it is in water and the part above the water is greater than or equal to $3$ metres. Find the length of the shortest pole.

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