University:
High School
Course:
High School Mathematics
Academic year:

2022
Views:

61

Pages:

2
Author:

camisants7m6n

Writing & Graphing Inequalities Vocabulary Inequality: Symbols used to compare expressions (e.g., <, >, ≤, ≥) Solution of an inequality: Is usually a set of numbers (not just one) Solution set: The range of all possible numbers that will make the inequality work Graph of an inequality: A visual representation of the solution set (see below) Core Concepts Representing Linear Equations Words: "x is equal to 2" Algebra: x = 2 Graph: A single point on the number line at 2 Representing Linear Inequalities Words: "x is less than 2" Algebra: x < 2 Graph: A number line with an open dot at 2 and an arrow pointing to the left Words: "x is greater than 2" Algebra: x > 2 Graph: A number line with an open dot at 2 and an arrow pointing to the right Words: "x is less than or equal to 2" Algebra: x ≤ 2 Graph: A number line with a closed dot at 2 and an arrow pointing to the left Words: "x is greater than or equal to 2" Algebra: x ≥ 2 Graph: A number line with a closed dot at 2 and an arrow pointing to the right Section 1: Writing Inequalities from Words Twelve is greater than or equal to five times a number. 12 ≥ 5n One-third of a number h is less than 15. 1/3h < 15 Seven is less than or equal to the difference of a number q and 6. 7 ≤ q - 6 The sum of a number n and 14 is more than 6. n + 14 > 6 Section 2: Determining Solutions of Inequalities d - 7 < 12; d = 19 19 - 7 < 12 12 < 12 (False) 19 is not a solution 9 ≥ 3n + 6; n = 1 9 ≥ 3(1) + 6 9 ≥ 3 + 6 9 ≥ 9 (True) 1 is a solution Section 3: Graphing Inequalities on a Number Line x ≥ 3 Closed dot at 3, arrow pointing to the right x ≤ 4 Closed dot at 4, arrow pointing to the left x > -1 Open dot at -1, arrow pointing to the right x ≤ 1 Closed dot at 1, arrow pointing to the left Section 4: Writing Inequalities from Graphs Graph: Closed dot at 2, arrow pointing to the right Inequality: x ≥ 2 Graph: Open dot at 0, arrow pointing to the left Inequality: x < 0 Graph: Closed dot at -3, arrow pointing to the left Inequality: x ≤ -3 Graph: Open dot at 3, arrow pointing to the right Inequality: x > 3