Class 10 Exam > Class 10 Notes > Mathematics Class 10 ICSE > Worksheet: Linear Inequalities
Worksheet: Linear Inequalities | Mathematics Class 10 ICSE PDF Download
Section A: Very Short Answer Questions
Q1. Solve: 5x – 7 < 18, where x ∈ N.
Q2. Solve: 3x + 2 ≥ 11, x ∈ W.
Q3. Solve: -2x > -10, x ∈ Z.
Q4. Solve: 7 – x ≤ 3, x ∈ N.
Q5. Solve: 2x – 1 ≤ 7, x ∈ N.
Section B: Short Answer Questions
Q6. Solve: 4x – 9 < 11, x ∈ N.
Q7. Solve : x – 3 ≥ 2, x ∈ Z.
Q8. Solve: 12 – 3x ≥ 0, x ∈ N.
Q9. Solve: -4x + 6 < -2, x ∈ Z.
Q10. Solve: 3x – 5 ≤ 10 and 2x + 1 ≥ 3, x ∈ N.
Section C: Long Answer Questions
Q11. Solve: -2 < 2x – 5 ≤ 7, x ∈ Z.
Q12. Solve and graph: (x – 2)(x – 6) < 0, x ∈ R.
Q13. Solve: 3x + 4 ≥ 10 and 5 – x > 0, x ∈ N.
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FAQs on Worksheet: Linear Inequalities - Mathematics Class 10 ICSE
| 1. What are linear inequalities and how do they differ from linear equations? |  |
Ans.Linear inequalities are mathematical expressions that involve a variable and an inequality sign (such as <,>, ≤, or ≥), indicating that one side is not necessarily equal to the other. In contrast, linear equations use an equal sign (=) to show that two expressions are equivalent. For example, the linear inequality 2x + 3 > 7 differs from the linear equation 2x + 3 = 7, as the former represents a range of values for x that satisfy the inequality, while the latter has a single solution.
| 2. How can we graph linear inequalities on a coordinate plane? | |
Ans.To graph a linear inequality, first, treat it as a linear equation and graph the corresponding line. Use a dashed line for inequalities that do not include equality (such as < or="">) and a solid line for those that do (such as ≤ or ≥). Then, select a test point that is not on the line (commonly the origin, (0,0)), plug it into the inequality, and determine if it satisfies the condition. If it does, shade the region of the graph that includes the test point; if not, shade the opposite region.
| 3. What are the steps to solve a system of linear inequalities? | |
Ans.To solve a system of linear inequalities, follow these steps:
1. Graph each inequality on the same coordinate plane, using the appropriate line style (dashed or solid) and shading for the solution regions.
2. Identify the overlapping shaded region where all inequalities are satisfied.
3. The solution set will be the coordinates within this overlapping region, representing all possible solutions that satisfy all inequalities in the system.
| 4. Can you provide a real-life example where linear inequalities are used? | |
Ans.Linear inequalities can be applied in various real-life situations, such as budgeting. For instance, if a person has a monthly budget of $500 for groceries and wants to allocate at least $200 but no more than $300 for dining out, this can be represented with the inequality 200 ≤ D ≤ 300, where D is the amount spent on dining. This provides a clear range of acceptable spending that keeps the overall budget intact.
| 5. What is the significance of the solution set of a linear inequality? | |
Ans.The solution set of a linear inequality is significant because it represents all possible values that satisfy the inequality. This set can be used in various applications, such as optimization problems in economics, engineering, and resource allocation. Understanding the solution set allows for informed decision-making based on constraints established by the inequality, helping individuals or organizations operate within defined limits.</,>
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Sep 29, 2025
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