# 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,

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