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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