![]() If we translate 7 is greater than 5 into algebraic expression, it will be 7 > 5. The statement “at most” simply means the value of the variable is less than or equal to and “at least” means the value of the variable is greater than or equal to. Don’t get confused with the statements “at most” and “at least”.Thus, if we translate it into algebraic expressions, this will become x + 7. However, the statement “ x more than 7” refers to adding 7 to the value of x. Hence, translating it to symbols will result to x > 7. While they may have the same meaning, “ x is greater than 7” refers to the value of x being greater than 7. Say for example you see the statements “ x is greater than 7” and “ x more than 7”. Sometimes the synonyms of greater than and less than can confuse you.However, these are the techniques that one must remember to avoid confusion. Translating mathematical statements into inequality can sometimes be confusing and difficult. TRANSLATING MATHEMATICAL STATEMENTS INTO INEQUALITY Therefore, the solution set is defined by (−4,5]. Since we have, it means only 5 is included in the solution set. Then, we can say that -4 is the lower limit and 5 is the upper limit. When we see notations such as a ≤ b ≤ c or a ≤ b −4. Thus, the solution set of $x\leq 3$ is ($-\infty,3$]. To write the solution set of $x\leq 3$, we use the symbols to indicate that the value of 3 is included. The figure below shows how you can easily spot an inequality that denotes greater than. To graph the inequality greater than, use an open circle to mark the starting value and point the arrow towards the positive infinity. INEQUALITY IN NUMBER LINE GRAPHING GREATER THAN IN A NUMBER LINE DIVISION PROPERTYįor any real numbers a, b, and $c\neq 0$, Take note that every time you multiply an inequality with negative number, you must reverse the inequality symbol. Subtraction property of inequality states that if a common constant term c is subtracted to both sides of inequality, then, for any real number a, b, and c: if □ 9, using the addition property of inequality, it follows that:.In addition property of inequality, if a common constant term c is added to both sides of inequality then, for any real number a, b, and c: Suppose 21 > 19 and 19 > 8, then by transitive property of inequality, 21 > 8. Which means, for any real numbers a and b, □ □ and □ ≤ □ and □ ≥ □ are equivalent, or we can simply say that: Since we know that 9 is larger than 8, then we can say that the only true statement is 8, ≤ and ≥ are each other’s converse. Suppose we have the statements, 8 9, only of it is true. Looking at the photo, we can say that the right-hand side has more ice cream than the left-hand side. The figure below shows the symbol used to denote greater than. Greater than is one of the inequalities used when a quantity is larger or bigger than the other quantity or quantities. ![]() Pierre Bouguer, a French mathematician put a line under the inequality symbols to represent greater than or equal to and less than or equal to. Harriot, a British mathematician died in 1621 and his book was published 10 years after his death. However, in 1631, the symbols for greater than and less than in the book “Artis Analyticae Praxis ad Aequationes Algebraicas Resolvendas” or The Analytical Arts Applied to Solving Algebraic Equations by Thomas Harriot was first introduced. Inequality as a mathematical concept is not a foreign concept to ancient mathematicians (Bagni, 2005) as they already knew the triangle inequality as a geometric fact and the arithmetic-geometric mean inequality (Fink, 2000). There are four inequality terms we can use to compare two quantities namely, greater than, greater than or equal to, less than, and less than or equal to. Inequalities can sometimes be presented as either question which can be solved or a statement of fact in the form of theorems. Inequality is a relationship between two numbers or algebraic expression which is not equal. TRANSLATING MATHEMATICAL STATEMENTS INTO INEQUALITY. ![]()
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