Solve the given inequation and write the solution set. 13 x - 5 < 15 x + 4 < 7 x + 12 , x ∈ R Represent the solution on a real number line.

Given, The inequation 13 x - 5 < 15 x + 4 < 7 x + 12 , x ∈ R Solving the equation 13 x - 5 < 15 x + 4 < 7 x + 12 Breaking the given equation in two parts. We get 13 x - 5 < 15 x + 4 15 x + 4 < 7 x + 12 Solving both the inequations one by one we get, 13 x - 5 < 15 x + 4 ∴ 13 x - 15 x < 5 + 4 ∴ - 2 x < 9 ∴ x > - 9 2 Now, solving 15 x + 4 < 7 x + 12 ∴ 15 x - 7 x < 12 - 4 ∴ 8 x < 8 ∴ x < 1 From the two values obtained the range of the x can be determined. Therefore, The solution is - 9 2 < x < 1 . represented as : = x : - 9 2 < x < 1 , x ∈ R Hence, solution is shown above.

Find the value of x , which satisfy the inequation - 2 5 6 < 1 2 - 2 x 3 ≤ 2 , ∀ x ∈ W and also represent the solution set on the number line.

Given, The inequation - 2 5 6 < 1 2 - 2 x 3 ≤ 2 , ∀ x ∈ W . Solving the inequation - 2 5 6 < 1 2 - 2 x 3 ≤ 2 Breaking the inequation in two parts - 2 5 6 < 1 2 - 2 x 3 1 2 - 2 x 3 ≤ 2 Solving the parts of the inequation one by one - 2 5 6 < 1 2 - 2 x 3 Converting the mixed fraction into improper fraction ⇒ - 17 6 < 1 2 - 2 x 3 Taking the LCM = 6 ⇒ - 17 6 < 1 × 3 2 × 3 - 2 x × 2 3 × 2 ⇒ - 17 6 < 3 6 - 4 x 6 Multiplying 6 to both the sides ⇒ - 17 < 3 - 4 x Transposing 3 to LHS ⇒ - 17 - 3 < - 4 x ⇒ - 20 < - 4 x Dividing the whole equation by 4 x < 5 _____(i) Now solving 1 2 - 2 x 3 ≤ 2 Taking LCM = 6 ⇒ 1 × 3 2 × 3 - 2 x × 2 3 × 2 ≤ 2 × 6 6 ⇒ 3 6 - 4 x 6 ≤ 12 6 Multiplying 6 to both the sides ⇒ 3 - 4 x ≤ 12 Transposing 3 to RHS ⇒ - 4 x ≤ 12 - 3 ⇒ - 4 x ≤ 9 Dividing both sides by 4 x ≥ - 9 4 _____(ii) From ( i ) and ( i i ) , - 9 4 ≤ x < 5 so the solution set of the inequation is 0 , 1 , 2 , 3 , 4 This solution can be shown on the number line as follows Hence, x : - 9 4 ≤ x < 5 , x ∈ W

E M B I B E

All In One ICSE Mathematics Class 10>Algebra>Chapter 4 - Linear Inequations>ARCHIVES (Last 8 Years)

Jitender Gupta and Divya Malik Solutions for Exercise 3: ARCHIVES (Last 8 Years)

Author:Jitender Gupta & Divya Malik

Jitender Gupta Mathematics Solutions for Exercise - Jitender Gupta and Divya Malik Solutions for Exercise 3: ARCHIVES (Last 8 Years)

Attempt the practice questions from Exercise 3: ARCHIVES (Last 8 Years) with hints and solutions to strengthen your understanding. All In One ICSE Mathematics Class 10 solutions are prepared by Experienced Embibe Experts.

Questions from Jitender Gupta and Divya Malik Solutions for Exercise 3: ARCHIVES (Last 8 Years) with Hints & Solutions

HARD

10th ICSE

IMPORTANT

All In One ICSE Mathematics Class 10>Chapter 4 - Linear Inequations>ARCHIVES (Last 8 Years)>Q 1

Solve the given equation, write down the solution set and represent it on the real number line.
$- 2 + 10 x \leq 13 x + 10 < 24 + 10 x, x \in Z$

MEDIUM

10th ICSE

IMPORTANT

All In One ICSE Mathematics Class 10>Chapter 4 - Linear Inequations>ARCHIVES (Last 8 Years)>Q 2

Solve the given inequation and represent the solution set on a number line.
$- 8 \frac{1}{2} < - \frac{1}{2} - 4 x \leq 7 \frac{1}{2}, x \in I$

HARD

10th ICSE

IMPORTANT

All In One ICSE Mathematics Class 10>Chapter 4 - Linear Inequations>ARCHIVES (Last 8 Years)>Q 3

Solve the given inequation, also write the solution set and represent it on the number line.
$- 3 (x - 7) \geq 15 - 7 x > \frac{x + 1}{3}, x \in R$

MEDIUM

10th ICSE

IMPORTANT

All In One ICSE Mathematics Class 10>Chapter 4 - Linear Inequations>ARCHIVES (Last 8 Years)>Q 4

Solve the given inequation and write the solution set.
$13 x - 5 < 15 x + 4 < 7 x + 12, x \in R$
Represent the solution on a real number line.

MEDIUM

10th ICSE

IMPORTANT

All In One ICSE Mathematics Class 10>Chapter 4 - Linear Inequations>ARCHIVES (Last 8 Years)>Q 5

Find the value of $x$ , which satisfy the inequation $- 2 \frac{5}{6} < \frac{1}{2} - \frac{2 x}{3} \leq 2, \forall x \in W$ and also represent the solution set on the number line.

MEDIUM

10th ICSE

IMPORTANT

All In One ICSE Mathematics Class 10>Chapter 4 - Linear Inequations>ARCHIVES (Last 8 Years)>Q 6

Solve the given inequation and write the solution set. Also, represent the solution set on the number line.
$\frac{- x}{3} \leq \frac{x}{2} - 1 \frac{1}{3} < \frac{1}{6}, x \in R$