Find the solution set of the inequation: x + 5 ≤ 2 x + 3 , x ∈ R . Graph the solution set on the number line.

Given inequation, x + 5 ≤ 2 x + 3 ⇒ x - 2 x ≤ 3 - 5 ⇒ - x ≤ - 2 ⇒ x ≥ 2 As x ∈ R Thus, the solution set is 2 , 3 , 4 , 5 , . . . . . Representing the solution on a number line:

If x ∈ R (real numbers) and - 1 < 3 - 2 x ≤ 7 , find solution set and represent it on a number line.

Given inequation, - 1 < 3 - 2 x ≤ 7 ⇒ - 1 - 3 < - 2 x ≤ 7 - 3 ⇒ - 4 < - 2 x ≤ 4 ⇒ - 4 2 < - 2 x 2 ≤ 4 2 ⇒ - 2 < - x ≤ 2 ⇒ - 2 ≤ x < 2 The solution set is x : x ∈ R , - 2 ≤ x < 2 Representing the solution on a number line:

Solve the inequation: 5 x + 1 7 - 4 x 7 + 2 5 ≤ 1 3 5 + 3 x - 1 7 , x ∈ R .

Given, 5 x + 1 7 - 4 x 7 + 2 5 ≤ 1 3 5 + 3 x - 1 7 5 x + 1 7 - 4 x 7 + 2 5 ≤ 8 5 + 3 x - 1 7 Multiply by LCM of 7 and 5 i.e., 35 25 x + 5 - 4 5 x + 14 ≤ 56 + 15 x - 5 ⇒ 25 x + 5 - 20 x - 56 ≤ 56 - 5 - 5 + 56 ⇒ - 10 x ≤ 102 - x ≤ 102 10 ⇒ - x ⩽ 51 5 ⇒ x ≥ - 51 5 ∵ x ∈ R ∴ Solution set = x : x ∈ R ≥ - 51 5

Find the range of values of x , which satisfy 7 ≤ - 4 x + 2 < 12 , x ∈ R . Graph these values of x on the real number line.

7 ≤ - 4 x + 2 < 12 7 < - 4 x + 2 and - 4 x + 2 < 12 4 x ≤ 2 - 7 and - 4 x < 12 - 2 4 x ≤ - 5 and - 4 x < 10 x ≤ - 5 4 and - x < 10 4 x ≤ - 5 4 and - x < 5 2 or x > - 5 2 ∵ x ∈ R ∴ Solution set - 5 2 < x ≤ - 5 2 = x : x ∈ R , - 5 2 < x ≤ - 5 4 Solution set on a number line

If x ∈ R , solve 2 x - 3 ≥ x + 1 - x 3 > 2 5 x . Also represent the solution on the number line.

Given, 2 x - 3 ≥ x + 1 - x 3 > 2 5 x ⇒ 2 x - 3 ≥ x + 1 - x 3 and x + 1 - x 3 > 2 5 x ⇒ 2 x - 3 ≥ 3 x + 1 - x 3 and 3 x + 1 - x 3 > 2 5 x ⇒ 6 x - 9 ≥ 3 x + 1 - x and 15 x + 5 - 5 x > 6 x ⇒ 6 x - 3 x + x ≥ 1 + 9 and 15 x - 6 x - 5 x > - 5 ⇒ 4 x ≥ 10 and 4 x > - 5 ⇒ x ≥ 10 4 and x > - 5 4 ∴ x ≥ 5 2 ∵ x ∈ R ∴ Solution set = x : x ∈ R , x ≥ 5 2 The solution set on the number line

E M B I B E

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

M L Aggarwal Solutions for Exercise 3: Chapter Test

Author:M L Aggarwal

M L Aggarwal Mathematics Solutions for Exercise - M L Aggarwal Solutions for Exercise 3: Chapter Test

Attempt the practice questions from Exercise 3: Chapter Test 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 3: Chapter Test with Hints & Solutions

MEDIUM

10th ICSE

IMPORTANT

Understanding ICSE Mathematics Class 10>Chapter 4 - Linear Inequations>Chapter Test>Q 2

Solve the inequation: $6 x - 5 < 3 x + 4, x \in I$ .

MEDIUM

10th ICSE

IMPORTANT

Understanding ICSE Mathematics Class 10>Chapter 4 - Linear Inequations>Chapter Test>Q 3

Find the solution set of the inequation: $x + 5 \leq 2 x + 3, x \in R$ . Graph the solution set on the number line.

MEDIUM

10th ICSE

IMPORTANT

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

If $x \in R$ (real numbers) and $- 1 < 3 - 2 x \leq 7$ , find solution set and represent it on a number line.

MEDIUM

10th ICSE

IMPORTANT

Understanding ICSE Mathematics Class 10>Chapter 4 - Linear Inequations>Chapter Test>Q 5

Solve the inequation: $\frac{5 x + 1}{7} - 4 (\frac{x}{7} + \frac{2}{5}) \leq 1 \frac{3}{5} + \frac{3 x - 1}{7}, x \in R$ .

HARD

10th ICSE

IMPORTANT

Understanding ICSE Mathematics Class 10>Chapter 4 - Linear Inequations>Chapter Test>Q 6

Find the range of values of $x$ , which satisfy $7 \leq - 4 x + 2 < 12, x \in R$ . Graph these values of $x$ on the real number line.

HARD

10th ICSE

IMPORTANT

Understanding ICSE Mathematics Class 10>Chapter 4 - Linear Inequations>Chapter Test>Q 7

If $x \in R$ , solve $2 x - 3 \geq x + \frac{1 - x}{3} > \frac{2}{5} x$ . Also represent the solution on the number line.

MEDIUM

10th ICSE

IMPORTANT

Understanding ICSE Mathematics Class 10>Chapter 4 - Linear Inequations>Chapter Test>Q 8

Find positive integers which are such that if $6$ is subtracted from five times the integer then the resulting number cannot be greater than four times the integer.

HARD

10th ICSE

IMPORTANT

Understanding ICSE Mathematics Class 10>Chapter 4 - Linear Inequations>Chapter Test>Q 9

Find three smallest consecutive natural numbers such that the difference between one-third of the largest and one-fifth of the smallest is atleast $3$ .

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