A solution set is the set of values which satisfy a given inequality. It means, each and every value in the solution set will satisfy the inequality and no other value will satisfy the inequality.
Example:
Solve 2x + 3 ≤ 7, where x is a natural number.
Solution:
2x + 3 ≤ 7
Subtracting 3 from both the sides,
2x ≤ 4
Dividing both sides by 2,
x ≤ 2
Since x is a natural number,
Solution set = {1,2}.
Number line:
The solutions of an inequality can be represented on a number line which is shown in the following examples.
Example:
Represent the solution set of inequality x + 4 ≤ 8, where ‘x’ is a whole number.
Solution:
Subtracting 4 from both sides of given inequality,
x ≤ 4
Since x is a whole number,
Solution set = {0,1,2,3,4}
Its number line representation is,
Example 2:
Represent the solution set of inequality -7≤ 3x+2 ≤ 11, where x is a real number.
Solution:
Subtracting 2 from the given inequality,
-9≤ 3x ≤ 9
Dividing the above inequality by 3,
-3 ≤ x ≤ 3
Since x is a real number,
Solution set = {-3,….,0,…,3}
Its number line representation is,
SchoolTutoring Academy is the premier educational services company for K-12 and college students. We offer tutoring programs for students in K-12, AP classes, and college. To learn more about how we help parents and students in El Monte visit: Tutoring in El Monte.