Notes from Tuesday Graphing Inequalities For certain questions, you will get an inequality and a replacement set to “test” each number to see if it makes the inequality true. Replacement set: the numbers you supposed to replace the variable with to “test” to see if the inequality is true or false Solution Set: the numbers from the replacement set that make the inequality true Solution: When a number is used in place of the x in the inequality and it makes the inequality true, we call it a solution. For example, Equation: X - 3 < 5 Replacement Set: [ 5, 7, 8 ] (this will be given to you as a part of the question) 1. You will solve the inequality by replacing the x with 6, 7, and then 8. X-3<5 (6) - 3 < 5 3<5 This is TRUE because 3 is less than 5. Therefore, the value of 6 is a solution to the inequality. The value of 6 will be a part of the solution set because it is an answer that makes the inequality correct. X-3<5 (7) - 3 < 5 4<5 This is TRUE because 4 is less than 5. Therefore, the value of 7 is a solution to the inequality. The value of 7 will be a part of the solution set because it is an answer that makes the inequality correct. X-3<5 (8) - 3 < 5 5<5 This is NOT true because 5 is not less than 5, it is equal to 5. Therefore, the value of 8 is not a possible solution for the inequality and 8 will NOT be a part of the solution set. After testing each number in the replacement set we have found that 6 and 7 make the inequality true when replaced for x, but 8 does not make the inequality true so it will not be apart of the solution set. For this problem, you will record that the solution set for this inequality, with the replacement set given will be (6,7). Graphing Inequalities on a Number Line When we are graphing inequalities on a number line, it is important to note what type of inequality is being used in that inequality. Less than < When you see the less than symbol then the dot you are plotting on the number line is OPEN. Greater than > When you see the less than symbol then the dot you are plotting on the number line is OPEN. The open dots represent that the number on the number line DOES NOT make the inequality true. Less than or equal to ≤ When you see the less than or equal to symbol, the dot you are plotting on the number line is CLOSED. Greater than or equal to ≥ When you see the greater than or equal to symbol, the dot you are plotting on the number line is CLOSED. The closed dot represents that the number on the number line DOES make the inequality true. For greater than AND greater than or equal to… draw a line from your dot to the RIGHT side of the number line. For less than AND less than or equal to… draw a line from your dot to the LEFT of the number line. Here is a website with videos that may also help… https://www.shmoop.com/study-guides/math/basic-algebra/graphing-inequalities
