Shading (One-Variable Inequality)
See It in Action
Two examples of the idea done right—and one common look-alike that is not right.
EXAMPLE
EXAMPLE
NON-EXAMPLE
Definition
"Shading" is a graphical method used to represent the solutions of one-variable inequalities on a number line. Here’s a detailed explanation:
Purpose: Shading helps visually identify the range of values that satisfy the inequality. It shows which part of the number line represents the solution set.
Process:
Identify the Boundary Point: Determine the boundary point(s) of the inequality. This is the value at which the inequality expression equals a specific value.
Determine the Type of Inequality:
Strict Inequalities: For inequalities like x > 3 or x < 5, where the boundary point is not included, use an open circle at the boundary point and shade to the right (for x >) or to the left (for x <).
Non-Strict Inequalities: For inequalities like x > 3 or x < 5, where the boundary point is included, use a closed circle at the boundary point and shade to the right (for x) or to the left (for x).
Shading Directions:
For x > a: Use an open circle at a and shade all values to the right of a.
For x > a: Use a closed circle at a and shade all values to the right of a.
For x < a: Use an open circle at a and shade all values to the left of a.
For x < a: Use a closed circle at a and shade all values to the left of a.
Example:
For the inequality x > 4:
Plot the number 4 on a number line.
Draw a closed circle at 4.
Shade everything to the right of 4.
For the inequality x < 2:
Plot the number 2 on a number line.
Draw an open circle at 2.
Shade everything to the left of 2.
In summary, shading on a number line is a visual technique used to represent all the possible solutions of an inequality, making it easier to understand and communicate the solution set.