Linear Inequation Video Lecture | Mathematics Class 10 ICSE

Ans. A linear inequation is a mathematical expression that represents a relationship between variables where one side is not strictly equal to the other, often using symbols such as <,>, ≤, or ≥. In contrast, a linear equation is an expression where the two sides are equal, represented by the equals sign (=). For example, the inequation 2x + 3 < 7="" suggests="" that="" 2x="" +="" 3="" can="" take="" on="" values="" less="" than="" 7,="" while="" the="" equation="" 2x="" +="" 3="7" states="" that="" 2x="" +="" 3="" is="" exactly="" equal="" to="" 7.=""

="" ans.="" to="" solve="" a="" linear="" inequation,="" follow="" these="" steps:="" 1.="" isolate="" the="" variable="" on="" one="" side="" of="" the="" inequation.="" this="" can="" be="" done="" by="" performing="" the="" same="" operations="" on="" both="" sides="" (addition,="" subtraction,="" multiplication,="" or="" division).="" 2.="" if="" you="" multiply="" or="" divide="" by="" a="" negative="" number,="" reverse="" the="" direction="" of="" the="" inequality="" symbol.="" 3.="" once="" isolated,="" express="" the="" solution="" in="" interval="" notation="" or="" as="" a="" number="" line="" representation="" indicating="" the="" range="" of="" possible="" values="" for="" the="" variable.=""

="" ans.="" the="" graphical="" representation="" of="" a="" linear="" inequation="" is="" a="" region="" of="" the="" coordinate="" plane="" that="" satisfies="" the="" inequation.="" for="" example,="" if="" you="" have="" the="" inequation="" y=""> 2x + 1, you would graph the line y = 2x + 1 as a dashed line (indicating that points on the line are not included) and shade the region above the line where y is greater than 2x + 1. The shaded area represents all the possible solutions to the inequation.

Ans. Linear inequations can be classified into four types based on the inequality symbols used: 1. Strictly less than ( < )="" 2.="" strictly="" greater="" than="" (=""> ) 3. Less than or equal to ( ≤ ) 4. Greater than or equal to ( ≥ ) Each type affects how the solution set is represented graphically and affects whether boundary points are included in the solution.

Ans. Understanding linear inequations is crucial because they model various real-world scenarios, such as budgeting, resource allocation, and optimization problems. For instance, in business, a company may need to determine the maximum number of products it can produce within a budget constraint, represented by a linear inequation. Mastery of these concepts allows individuals to make informed decisions based on constraints and available resources.</,>