Write inequalities from number lines

Learning Objectives Identify the key components of an inequality represented on a number line (circle type, shading direction, and value). Distinguish between strict inequalities (<, >) and inclusive inequalities (≤, ≥) based on open and closed circles. Correctly determine the direction of the inequality symbol based on the shaded region of the number line. Write a one-variable inequality that accurately represents a given number line graph. Interpret number lines with different scales and use the correct numerical value in their inequalities. Write compound inequalities for number lines showing a segment between two points. Ever wondered how to describe a range of possibilities, like 'temperatures above 0°C' or 'ages 13 and older' using math? 🌡️ Nu...

TermDefinitionExample InequalityA mathematical statement that compares two expressions using an inequality symbol (like <, >, ≤, or ≥), showing that one quantity is not necessarily equal to another.$$x > 5$$ (x is greater than 5) Number LineA visual representation of numbers as points on a straight line, ordered from least to greatest, used to graph inequalities.A line with integers marked, and a specific point or region highlighted. Open Circle (or Unfilled Circle)A circle on a number line that is not filled in, indicating that the endpoint number is NOT included in the solution set of the inequality.An open circle at 3 means the solution is all numbers *close to* 3 but not including 3 itself, like 3.0001 or 2.999. Closed Circle (or Filled Circle)A circle on a number line that i...

Rule for Open Circles An open circle on a number line corresponds to a strict inequality symbol: less than ($$<$ $) or greater than ($$>$ $). If the endpoint is not included in the solution, use < or >. For example, an open circle at 'a' shaded right means $$x > a$$, and shaded left means $$x < a$$. Rule for Closed Circles A closed circle on a number line corresponds to an inclusive inequality symbol: less than or equal to ($$\le$$) or greater than or equal to ($$\ge$$). If the endpoint is included in the solution, use ≤ or ≥. For example, a closed circle at 'a' shaded right means $$x \ge a$$, and shaded left means $$x \le a$$. Rule for Shading Direction The direction of the shaded region indicates the direction of the inequality....