# 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.*Subtracting***Solution:****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.