{"id":10311,"date":"2026-07-03T17:39:42","date_gmt":"2026-07-03T17:39:42","guid":{"rendered":"https:\/\/kapdec.com\/help\/?p=10311"},"modified":"2026-07-03T17:39:42","modified_gmt":"2026-07-03T17:39:42","slug":"understanding-expressions-and-system-of-linear-inequalities","status":"publish","type":"post","link":"https:\/\/kapdec.com\/help\/understanding-expressions-and-system-of-linear-inequalities\/","title":{"rendered":"Understanding Expressions And System Of Linear Inequalities"},"content":{"rendered":"
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KAPDEC® | Elite STEM Learning Platform | https:\/\/kapdec.com<\/a><\/p>\n

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Source: Kapdec.com<\/p>\n<\/div>\n

Unit: Expressions and System of Equations<\/strong><\/h2>\n

Understanding Expressions and System of Linear Inequalities<\/strong><\/h3>\n

Expressions:<\/strong><\/p>\n

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  1. Basics:<\/strong> Expressions are mathematical phrases that combine numbers, variables, and operations (like addition, subtraction, multiplication, and division).<\/li>\n
  2. Types:<\/strong>\n
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    • Algebraic:<\/strong> Contains variables and constants.<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n

      \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0Example: 3x + 5.<\/p>\n

      \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0Numeric:<\/strong> Purely numerical, without variables.<\/p>\n

      \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 Example: 12 – 4.<\/p>\n

      Types of Expressions:<\/strong><\/p>\n

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      • Monomial:<\/strong> Single term expression (e.g., 3x, -7).<\/li>\n
      • Binomial:<\/strong> Two terms expression (e.g., 2x + 5, y – 1).<\/li>\n
      • Trinomial:<\/strong> Three terms expression (e.g., x2<\/sup> + 3x – 4, a + b + c).<\/li>\n
      • Polynomial:<\/strong> Any expression with multiple terms (can include monomial, binomial, trinomial).<\/li>\n<\/ul>\n
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        1. Components:<\/strong>\n
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          • Variables:<\/strong> Represented by letters and can take different values.<\/li>\n
          • Constants:<\/strong> Fixed values.<\/li>\n
          • Operators:<\/strong> Symbols like +, -, \u00d7, \u00f7, representing operations.<\/li>\n<\/ul>\n<\/li>\n
          • Evaluating Expressions:<\/strong>\n
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            • Substitute the values of variables and simplify using order of operations (PEMDAS\/BODMAS).<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n
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              • PEMDAS:<\/strong> Parentheses, Exponents, Multiplication and Division (left to right), Addition and Subtraction (left to right)<\/li>\n
              • BODMAS:<\/strong> Brackets, Orders (exponents), Multiplication and Division (left to right), Addition and Subtraction (left to right)<\/li>\n<\/ul>\n

                Systems of Linear Inequalities:<\/strong><\/p>\n

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                1. Definition:<\/strong> A set of linear inequalities involving the same set of variables.<\/li>\n
                2. Linear Inequality:<\/strong> An inequality that can be written in the form ax + by \u2264 c or ax + by \u2265 c.<\/li>\n
                3. Graphical Representation:<\/strong>\n
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                  • Each inequality corresponds to a shaded region on the coordinate plane.<\/li>\n
                  • The solution is the overlapping\/shaded region common to all inequalities.<\/li>\n<\/ul>\n<\/li>\n
                  • Solution Methods:<\/strong>\n
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                    • Graphical Method:<\/strong> Plot each inequality on the coordinate plane and find the overlapping region.<\/li>\n
                    • Algebraic Method:<\/strong> Solve each inequality separately and then find the common solution region.<\/li>\n<\/ul>\n<\/li>\n
                    • Types of Solutions:<\/strong>\n
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                      • Feasible Region:<\/strong> The set of points that satisfy all the given inequalities.<\/li>\n
                      • Bounded Region:<\/strong> When the feasible region is finite.<\/li>\n
                      • Unbounded Region:<\/strong> When the feasible region extends indefinitely.<\/li>\n<\/ul>\n<\/li>\n
                      • Testing Solutions:<\/strong>\n
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                        • Substitute test points into the original inequalities to check if they satisfy all conditions.<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n

                          Key Tips for Revision:<\/strong><\/p>\n

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                          1. Practice evaluating various types of expressions.<\/li>\n
                          2. Understand the graphical representation of linear inequalities.<\/li>\n
                          3. Practice solving systems of linear inequalities both graphically and algebraically.<\/li>\n
                          4. Test solutions to ensure they satisfy all conditions.<\/li>\n<\/ol>\n

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