Types of Inequalities in Maths

Equations in mathematics aren’t usually about balancing both sides with a ‘equal to’ sign. It’s sometimes about a ‘not equal to’ relationship, when something is larger than or less than the other. In mathematics, an inequality is a relationship that compares two numbers or other mathematical expressions in a non-equal way. Inequalities are mathematical expressions that fall within the category of algebra.

Let’s learn about inequalities, their principles, and how to solve and graph them.

Definition of inequalities

Inequalities are mathematical expressions with unequal sides on both sides. Unlike equations, we compare two values in inequality. Between the equal signs, less than (or less than or equal to), greater than (or more than) replaces the equal sign (more than or equal to), or sign (not equal to).

Somu has been chosen for the 12U Softball team. Somu’s age is unknown. Because it doesn’t mention “equals,” you don’t know Somu’s age. You do know, however, that her age should be less than or equal to 12, so Somu’s Age 12 can be written. This is a real-world example of disparities.

Types of Inequalities

P ≠ q indicates that p is not the same as q, 

p < q indicates that p is less than q and 

p > q indicates that p is more than q.

The expression p ≤ q denotes that p is less than or equal to q.

The expression p ≥  denotes that p is greater than or equal to q.

Inequalities come in a variety of forms. The following are some of the most significant inequalities:

• Polynomial inequalities 

• Absolute value inequalities

• Rational inequalities

Characteristics of inequalities

Inequalities have their own set of rules. Here are a few examples of inequality.

Rule 1: Inequalities

You can jump over the intermediate inequality when inequalities are linked together.

If p < q and q < d are true, then p < d is true.

If p is greater than q and q is greater than d, then p is greater than d.

For instance, If Satya is older than Dona and Dona is older than Satya, Satya must be older.

Rule 2: Inequalities

When the numbers p and p are swapped, the result is:

If p is greater than q, then q is greater than p.

If p > q is true, then q < p is true.

For instance, because Arijit is older than Shree, Shree is younger than Arijit.

Rule 3: Inequalities

If we add a number d to both sides  the inequality If p < q, then p + d < q + d

Satya, for example, has less money than Dona. Even if satya  and dona each receive an additional $5, Oggy will still have less money than Mia.

Likewise:

• If the expression holds p < q, then p – d < q – d

• If the expression holds p > q, then p + d > q + d, and

• If the expression holds p > q, then p – d > q – d

As a result, adding and subtracting the same value from both p and q has no effect on the inequality.

Rule 4: Inequalities

There is no change in inequality if you multiply numbers p and q by a positive value. When both p and q are multiplied by a negative amount, the inequality changes: After multiplying by, p < q becomes q < p after Multiplying by (-2)

The following are the rules:

• If p < q, and d is positive, then pd < qd

• If p < q, and d is negative, then pd > qd (inequality swaps)

Example of a positive case: Oggy’s score of 5 is less than Mia’s score of 9 (p < q). Even if Oggy and Mia double their scores, 2p < 2q, Oggy’s score will be lower than Mia’s. If the scores go negative, the scores will be -p > -q.

Rule 5: Inequalities

The direction of the inequality is changed by putting minuses in front of p and q.

• If p < q, then -p > -q.

• If p > q, then -p < -q

• It’s the same as multiplying by (-1) except it’s in the opposite way.

Rule 7 : Inequalities 

The square of a given number is always greater than or equal to zero i.e. p² ≥ 0.

5² = 25 , (-9)² = 81 , 7² = 49 , (-7)² = 49

Rule 8 : Inequalities

The inequality doesn’t change when we take the square root of numbers related by Inequalities.

 If the numbers hold this inequality p ≤ q, then √p ≤ √q (for p, q ≥ 0).

If we have 5 < 7 then √5 < √7 inequality holds true.

Conclusion 

In mathematics, an inequality is a mathematical expression that has two sides that are not equal. In mathematics, inequality occurs when a connection performs a non-equal comparison between two expressions or two numbers. In this case, the inequality symbols greater than symbol (>), less than symbol (<), greater than or equal to symbol (≥), less than or equal to symbol (≤), or not equal to symbol (≠) replace the equal sign “=” in the expression.