Solution Set (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
The "solution set" for a one-variable inequality is the set of all values that satisfy the inequality. It represents all possible values for the variable that make the inequality true. Here’s a more detailed explanation:
Definition: The solution set is the collection of values that, when substituted into the inequality, make it a true statement. For example, if you have the inequality x < 5, the solution set includes all values of x that are less than or equal to 5.
Determining the Solution Set:
Solve the Inequality: To find the solution set, you need to solve the inequality. This involves isolating the variable on one side of the inequality.
Describe the Range: Once solved, the solution set can be described graphically on a number line.
Examples:
Inequality: x > 3
Solution Set: All values greater than 3. On a number line, you would shade to the right of 3, using an open circle at 3.
Inequality: x < 4
Solution Set: All values less than or equal to 4. On a number line, you would shade to the left of 4, using a closed circle at 4.
In summary, the solution set of a one-variable inequality includes all values that satisfy the inequality, and it can be represented graphically on a number line.