Linear ineq.pptx linear inequalities presentation

Maths

1. LINEAR INEQUALITIES MADE BY: HONEY BHOWMICK PGT-APS DIGHI

2. LEARNING OBJECTIVES: Understand the concept of linear inequality. Know the application of linear inequality in real life . Understand the rules of solving linear inequalities. Solve the different types of questions based on linear inequality.

3. 1. Physics: In mechanics, linear inequalities can model constraints on physical systems, such as forces or velocities, and help solve problems involving equilibrium and motion. In thermodynamics, linear inequalities can represent constraints on the properties of gases, such as pressure, volume, and temperature. 2.Engineering: Engineers use linear inequalities to model constraints in optimization problems, such as maximizing or minimizing certain parameters while satisfying certain limitations. In electrical engineering, linear inequalities can be used to represent limits on voltage, current, or power in various circuits. 3.Computer Science: In computer programming and algorithms, linear inequalities are used in optimization problems and to define the feasible region for certain variables. In computer graphics, linear inequalities are used to define clipping regions and visible areas on a screen. 4. Environmental Science: Linear inequalities can be used to model environmental systems, such as the balance between pollution emissions and absorption processes in the atmosphere. 5. Social Sciences: Linear inequalities can be used in sociological and demographic studies to model inequalities in income distribution, wealth, or educational attainment. 6.Operations Research: Linear programming, a branch of operations research, extensively uses linear inequalities to optimize the allocation of resources and solve complex decision-making problems. 7.Economics: .Linear inequalities are commonly used to represent production possibilities frontiers in economics, where limited resources are allocated between the production of two goods. .In the study of consumer behavior, linear inequalities can represent budget constraints, showing the combinations of goods and services a consumer can afford.

4. NOTE DOWN: IN APPLICATION QUESTIONS USE: At least - At most - more than - > less than - <  

5. TYPE 2- QUESTIONS: SOLVE: C < AX+B < D OR C AX+B D OR C AX+B D  

6. TYPE3 QUESTIONS: SYSTEM OF LINEAR INEQUALITIES Ax +B >D , cx + e ≤ f While solving questions on finding the solution set using alg. method, first plot the given inequations on the number line and shade the region based on the inequality sign. The common region to the given inequations give the solution set. Questions can be asked based on finding solution set of system of linear inequations in two variables involving strict (<, >) and slack (≤,≥) inequalities.

7. RULES 1: MODULUS FUNCTIONS :

8. |x – a| < r |x – a| ≤ r |x – a| > r x < a – r or x > a + r |x – a| ≥ r x ≤ a – r or x ≥ a + r   RULES 2: Rules 3: a<|x|<b x a |x| b x [ b, a] [ a, b ] a<| x c|< b x a | x c | b x [ b+c, a+c ] [ a+c , b+c ]  

9. Try these questions:

10. TYPE 5 QUESTIONS: < k or > k or k or k Steps : 1. Transpose all the terms on LHS. Make it - k < 0 . 2. Make coeff . Of x positive in numerator and denominator if they are not. 3. Find the zeroes of num. and deno . ( Find Critical points) 4. Plot the critical points on number line. These critical points divides the number line in different regions. 5. Find the sign of the function in these regions. 6. Select the appropriate region on the basis of the sign of the inequation obtained in step1. Note Down: Never include critical pt. of denominator.( always come with open bracket)  

11. PRACTICE QUESTIONS:

12. Ans :