Solution Set of an Inequality

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.