{"id":9535,"date":"2026-06-01T21:33:48","date_gmt":"2026-06-01T21:33:48","guid":{"rendered":"https:\/\/kapdec.com\/help\/?p=9535"},"modified":"2026-06-02T22:54:56","modified_gmt":"2026-06-02T22:54:56","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":"\n\n\n
 <\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

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

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

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

    \n
  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
      \n
    • Algebraic:<\/strong> Contains variables and constants.<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n

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

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

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

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

        \n
      • 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
          \n
        1. Components:<\/strong>\n
            \n
          • Variables:<\/strong> Represented by letters and can take different values.<\/li>\n
          • Constants:<\/strong> Fixed values.<\/li>\n
          • Operators:<\/strong> Symbols like +, -, ×, ÷, representing operations.<\/li>\n<\/ul>\n<\/li>\n
          • Evaluating Expressions:<\/strong>\n
              \n
            • Substitute the values of variables and simplify using order of operations (PEMDAS\/BODMAS).<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n
                \n
              • 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

                  \n
                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 ≤ c or ax + by ≥ c.<\/li>\n
                3. Graphical Representation:<\/strong>\n
                    \n
                  • 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
                      \n
                    • 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
                        \n
                      • 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
                          \n
                        • 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

                            \n
                          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

                             <\/p>\n","protected":false},"excerpt":{"rendered":"

                              Unit: Expressions and System of Equations Understanding Expressions and System of Linear Inequalities Expressions: Basics: Expressions are mathematical phrases that combine numbers, variables, and operations (like addition, subtraction, multiplication, and division). Types: Algebraic: Contains variables and constants.                        Example: 3x + 5.     […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[635],"tags":[644,640,643,647,638,639,645,637,641,646,642],"class_list":["post-9535","post","type-post","status-publish","format-standard","hentry","category-sat-math","tag-college-admissions","tag-digital-sat","tag-high-school-students","tag-improve-sat-score","tag-sat-advanced-math","tag-sat-math-preparation","tag-sat-practice-questions","tag-sat-prep","tag-sat-reading-and-writing-sat-tutoring","tag-sat-strategies","tag-sat-test-preparation"],"_links":{"self":[{"href":"https:\/\/kapdec.com\/help\/wp-json\/wp\/v2\/posts\/9535","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/kapdec.com\/help\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/kapdec.com\/help\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/kapdec.com\/help\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/kapdec.com\/help\/wp-json\/wp\/v2\/comments?post=9535"}],"version-history":[{"count":1,"href":"https:\/\/kapdec.com\/help\/wp-json\/wp\/v2\/posts\/9535\/revisions"}],"predecessor-version":[{"id":9621,"href":"https:\/\/kapdec.com\/help\/wp-json\/wp\/v2\/posts\/9535\/revisions\/9621"}],"wp:attachment":[{"href":"https:\/\/kapdec.com\/help\/wp-json\/wp\/v2\/media?parent=9535"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/kapdec.com\/help\/wp-json\/wp\/v2\/categories?post=9535"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/kapdec.com\/help\/wp-json\/wp\/v2\/tags?post=9535"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}