MODULE 8

• equality in Mathematics is an idea where one (1) side justifies the end result (and vice versa). As a result, we call equality an equation because one (1) side of a Mathematical idea “equates” on the other side.
• inequality is an idea where one (1) side cannot justify the end result (and vice versa); as a result, one (1) side is always bigger than the other.
• Greater than. This represents the arrowhead that faces to the right, indicating that the number is at the right side of the number line. In other words, the open end faces the larger number
• Less than. This represents the arrowhead that faces to the left, indicating that the number is on the left side of the number line. In short, the arrow point indicates the smaller number opposite the number where the open end is facing.
• Greater (or Less) than or Equal to. This represents that a given inequality is either bigger than the other, or they may be equal. This is usually used in Algebra more than Arithmetic, as a variable can only prove the inequality’s validity if the variable is evaluated with a numerical value.
• expression is, where it is defined as the idea of expressing numbers through the use of variables without expressing their actual values.
• A phrase or a sentence fragment: expression
• The result is simplification: expression
• the answer is numerical value: expression
• Expression: A Mathematical idea that combines numbers, variables, and operators to define the value of something.
• Equation: A Mathematical idea wherein two (2) given terms are set equal to each other. However, should the result be false, then there is no solution.
• a complete sentence: equation
• result is solution: equation
• the answer is assertation: equation
• equation

  
• expression

  
• Simple Linear: An equation whose highest possible exponent is one (1). It also only involves one (1) variable.
• Simultaneous Linear: An equation whose highest possible exponent is one (1). It also involves two (2) different variables
• Quadratic: An equation whose highest possible exponent is two (2).
• Cubic: An equation whose highest possible exponent is three (3).
• a linear equation is an equation whose highest possible exponent value present in all affected terms is one (1)
• Addition: Same numbers may be added (or subtracted) to both sides of the equation, with the result being the solution to the equation. This is observed when 𝒂, 𝒃, and 𝒄 are real numbers, and if 𝒂 = 𝒃.
• Multiplication: Both sides of the equation will be multiplied (or divided) by the same nonzero number, with the result being an equivalent equation. This is observed when 𝒂, 𝒃, and 𝒄 are real numbers, and if 𝒂 = 𝒃.
• Reflexive: Any number is equal to itself
• Symmetric: Any side can be interchanged, but the idea remains the same.
• Transitive: If two (2) equations are equal to a third quantity, then they are all equal to each other.
• A linear inequality is formally defined as a mathematical statement that uses inequality symbols. Simply put, the final answer (or solution) of a linear inequality is a range of values rather than a specific value.
• Parenthesis: This indicates that the number that either follows this symbol (or precedes it) is not included in the established range of values. Infinity symbols are exempted. Some reference materials also use hollow circles instead of parentheses. This is usually used when the inequality either has > or <.
• Brackets: This indicates that the number that either follows this symbol (or precedes it) is also included in the established range of values. Infinity symbols are exempted. Some reference materials also use darkened circles instead of parentheses. This is usually used when the inequality either has ≥ or ≤.
• Arrow: Indicates all possible numbers that can satisfy the inequality, which extends to infinity. This is usually used when the inequality compares only two (2) terms.
• Line: This indicates that only certain numbers within its boundaries can satisfy the inequality, as it has definite endpoints. This is usually used when the inequality compares three (3) terms.
• Conditional: This equation can only be solved by certain numbers only.
• Identity: This equation is true regardless of the assigned value.
• Transitive: If one (1) value is larger than the second value, and the second is larger than the third, then the first value is greater than the third. The same is applied conversely.
• Same numbers may be added (or subtracted) to both sides of the equation, with the result being the solution to the equation. This is observed when 𝒂, 𝒃, and 𝒄 are real numbers.
• Multiplication: Both sides of the equation will be multiplied (or divided) by the same nonzero number, with the result being an equivalent equation. This is observed when 𝒂, 𝒃, and 𝒄 are real numbers.