Graphing Inequalities on a Number Line Calculator

An inequality compares two values, showing that one is less than, greater than, or equal to another. When graphing a single variable inequality like x > a on a number line, you first locate the boundary value 'a'. If the relation uses strictly 'greater than' (>) or 'less than' (<), you draw an open circle at 'a' to indicate that the boundary value is excluded from the solution set. If the relation includes 'or equal to' (≥ or ≤), you draw a closed (solid) circle to show that the value is included. Finally, you draw a directional ray pointing right for greater values or left for lesser values. Compound inequalities involve two conditions joined by 'and' or 'or', creating bounded intervals or diverging rays.

Let us graph the compound inequality: -2 < x ≤ 3. This statement contains two parts: x > -2 and x ≤ 3, joined by an 'and' condition. Step 1: Identify the boundary numbers on the number line, which are -2 and 3. Step 2: Plot an open circle at -2 because the inequality uses strict less than (<). Step 3: Plot a closed circle at 3 because the inequality uses less than or equal to (≤). Step 4: Draw a solid line segment connecting the two circles, indicating that all numbers between -2 and 3 satisfy both conditions simultaneously.

Always double-check your inequality symbol before drawing circles; confusing strict inequalities with inclusive ones is the most common plotting error. When multiplying or dividing both sides of an inequality by a negative number, remember to reverse the inequality sign direction before graphing. Practice breaking compound inequalities apart into two separate statements to easily determine whether the final graph will be a bounded segment or two outward-pointing rays.