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### Theory:

Earlier, we explored the linear equation. Where we learned 'what is an equation, and how we can solve it using various methods'.

Now we recall about equation; then we jump into the exciting topic called inequation.
Equation: The equation is a statement of equality that contains one or more unknown value or variables.
Example:
Consider the equation $$2x + 4 = 10$$;

If we substitute $$x = 4$$ we can get $$LHS = RHS$$. Therefore, the solution of $$x$$ for this equation is $$4$$.
Are you wondering how this equation concept related to the inequation?

Let me make it clear for you.

In the above equation, we can notice that $$LHS$$ $$(2x + 4)$$ and $$RHS$$ $$(10)$$ are equal, whereas, in the inequation, it does not plain and simple.

When an algebraic expression is equated on both sides, it will be called an equation; if it is not equated, it is known as inequation or inequality.
Inequation:
Let us see a situation to understand this concept.

Rajiv wanted to get a voter ID card. But as per norms, one should attain an age of $$18$$ to get a voter ID card. But Rajiv's age is lesser than $$18$$.

If we take Rajiv's age as $$(x)$$ and write the above statement in an algebraic inequation, we get:

$$x < 18$$. That means Rajiv's age is lesser than $$18$$.

If Rajiv's age is $$18$$, then the expression will be $$x = 18$$. But it does not.

Since the expression $$x < 18$$ is not an equal, this is not an equation; it is called inequation.
1. An algebraic statement that shows two algebraic expressions being unequal is called an algebraic inequation.

2. In general, when two expressions are compared, one might be; less than $$(<)$$, less than or equal to $$(≤)$$, greater than $$(>)$$, greater than or equal to $$(≥)$$ the other.

3. In an inequation, the algebraic expressions are connected by one out of the four signs of inequalities, namely, $$>$$, $$≥$$, $$<$$ and $$≤$$. Now we explore some examples of how we can use the inequation.
Example:
1. Sanjay is older than Riya

Let us consider Sanjay's age as $$(x)$$, and Riya's age be $$(y)$$. Since Sanjay is older than Riya, we should use the greater than $$(>)$$ symbol towards Sanjay. Therefore, the inequation will be $$x > y$$.

2. Veena's monthly income is not more than $$₹50000$$.

Consider Veena's salary as $$(x)$$. Since Veena's salary is not more than $$₹50000$$, her salary must be $$₹50000$$ or lesser than $$₹50000$$.

So, we should use the lesser than equal symbol $$(≤)$$ in the inequation.

Therefore, the inequation will be $$x ≤ ₹50000$$. 3. Kavitha said to her father that she would score $$70$$ mark or more than $$70$$ marks in the coming mathematics exam.

Say the mark she will score is $$(x)$$. She will score $$70$$ mark or more than $$70$$ marks; here, we can use greater than equal symbol to denote the inequation.

Hence, the inequation is $$x ≥ 70$$ marks.

Some more examples: Important!
• $$LHS$$ - stands for Left Hand Side
• $$RHS$$ - stands for Right Hand Side