Skip to main content

ICSE Solutions for Class 10 Mathematics – Solving Linear Inequations in One Variable

ICSE Solutions for Class 10 Mathematics – Solving Linear Inequations in One Variable

ICSE Solutions for Class 10 Mathematics – Solving Linear Inequations in One Variable


Formulae

Two permissible rules:

1. Addition – Subtraction Rule:
If the same number or expression is added to or subtracted from both sides of an inequation, the resulting inequation has the same solution (or solutions) as the original.

2. Multiplication – Division Rule:
(i) If both sides of an inequation are multiplied or divided by the same positive number, the resulting inequation has the same solution (or solutions) as the original.
(ii) If both sides of an inequation are multiplied or divided by the same negative number, the resulting inequation has the same solution (or solutions) as the original if the symbol of the inequality is reversed.
Thus, the only difference between solving a linear equation and solving an inequation concerns multiplying or dividing both sides by a negative number. Therefore, always reverse the symbol of an inequation when multiplying or dividing by a negative number.

3. Properties of absolute values:
 
 

Determine the Following

Question 1. Give that x ∈ I. Solve the inequation and graph the solution on the number line:
 
Question 2. Graph the solution set for each inequality:
 
 
Question 3. Solve the given inequation and graph the solution on the number line
 
Question 4. Given that x ∈ R, solve the following inequality and graph the solution on the number line:
 
Question 5. Given:
 
Question 6. Solve 2 ≤ 2x – 3 ≤ 5, x ∈ R and mark it on a number line.
 
 
Question 7. For each inequality, determine which of the given numbers are in the solution set:
 
Question 8. Graph the solution sets of the following inequalities:
 
Question 9. Solve the equation and represent the solution set on the number line.
 
Question 10. Solve the following inequation and represent the solution set on the number line:
 
Question 11. Solve the following in equalities and graph their solution set
 
 
Question 12. Solve the following inequation and graph the solution set,
 
Question 13. Solve the following inequation and graph the solution on the number line.
 
  
Question 14. Solve the following inequalities and represent the solution on a number line:
 
 
 
 
Question 15. Solve the following inequalities and represent the solution set on a number line:
 
 
 
 
Question 16. Solve the following inequation, write the solution set and represent it on the number line:
 
 
Question 17. Find the values of x, which satisfy the inequation
 
 
Question 18. Solve the following inequalities in the given universal set:
 
 
 
Question 19. Find the solution set of the following inequalities and draw the graph of their solutions sets:
 
 
 
 
Question 20. Solve the following inequalities and graph their solution set:
 
 


Comments

Post a Comment

Popular posts from this blog

ICSE Solutions for Class 9 Geography – Natural Regions of the World

ICSE Solutions for Class 9 Geography – Natural Regions of the World ICSE Solutions for Class 9 Geography – Natural Regions of the World Exercises I. Short Answer Questions. Question 1. Define the term ‘natural region’. Answer: A natural region refers to a part of Earth’s surface having a particular uniformity in physical and climatic elements. Question 2. Name any four natural regions of the world. Answer: Equatorial Region, Tropical Grasslands (Savanah), Tropical Monsoon type and Tropical Deserts. Question 3. Briefly state the importance of climate. Answer: Climate imparts an important effect on human life, as the life style, occupations, trade facilities all are deeply related to the climatic behaviour of a particular natural region. Climate has a remarkable impact on human efficiency too. Question 4. State the location of the Equatorial Region. Answer: It is found in Amazon basic, Congo basin and Indonesia etc. Question 5. What is the latitudinal extent of the Monsoon climate? Answe...
Post a Comment
Read more

ICSE Solutions for Class 8 History and Civics – The Growth of Nationalism

TIME TO LEARN I. Fill in the blanks: The Congress of Vienna was hosted by The Austrian Chancellor Duke Metternich . The American Revolution began in 1776. The first clear expression of nationalism came up with the French Revolution. The French Revolution began in 1789. England had Thirteen colonies in North America. American thinker Thomas Jefferson , asked the people to rebel against the tyrannical rule of England . A new country called The United States of America was born after the American Revolution. II. Match the contents of Column A and Column B: Answer:  III. State whether the following statements are true or false: The 13 colonies of North America were dissatisfied with the rule of the master country, England. (True) The French society was divided into three classes, each enjoying similar rights and privileges. (False)   The French Revolution began with the storming of Bastille in 1789. (True) A new constitution was framed by the French Assembly in 1785. (False) ...
Post a Comment
Read more

ICSE Solutions for Class 9 History and Civics – India in the 6th Century BC: Rise of Jainism and Buddhism

ICSE Solutions for Class 9 History and Civics – India in the 6th Century BC: Rise of Jainism and Buddhism ICSE Solutions for Class 9 History and Civics – India in the 6th Century BC: Rise of Jainism and Buddhism EXERCISES Question 1. Give any two sources to reconstruct the two great religious movements—Jainism and the Buddhism. Answer: Literary Sources: The Jataka Tales, The Tripitakas.  Archaeological Sources: The Great Stupa at Sanchi, Samath Pillar. Question 2. Mention two causes which favored the rise of Jainism and Buddhism in the 6th Century BC. Answer: Two causes which favored the rise of Jainism and Buddhism in the 6th Century BC. were: Ritualistic Vedic Religion. Expensive Sacrifices. Question 3. Name the first and the last two Jain Answer: The first Tirthankaras was ‘Risabit known as Adi Nath. The last two Tirathankaras were ‘Parashvanath’ and ‘Mahavira’. Question 4. What was the Original name of Mahavira? Answer: The Original name of Mahavira was Vardhamana. Question...
Post a Comment
Read more