What are the basic differences between equation and inequation?

We have seen that equations are expressed by sign of equality and inequations are expressed by sign of inequality. We have also seen that a linear equation has one root and quadratic equation has two roots. The equation, after simplification of terms, will show that the maximum power of the variable is equal to the variable is equal to number of roots. As the maximum power of x^2 + x - 2 = 0 is 2, so it has two roots namely 1 and -2. So, we see that the number of roots of an equation is definite but it is not true for inequation.

As for example, the inequation x < 5 is satisfied for any value of x less than 5, and the number of numbers less than 5 is infinite. Similarly, the inequation 2x – 3 ≥ 5 holds for an infinite number of values of x. Hence an inequation is satisfied by an infinite values of the unknown quantity. The set of values for which an inequation is satisfied is called the solution set of the inequation.

**Note:** An inequation with a given condition may have a finite number of solutions.

For example, for a positive integer, x ≤ 5 has the solution 1, 2, 3, 4, 5.

Hence we can denote the solution set of the inequation x ≤ 5 by {1, 2, 3, 4, 5}

**Simple inequation:** If an inequation contains an known quantity of power one only, it is called a simple inequation.

5x + 7 > 10, 6x – 8 ≥ 23, 5x + 3 ≤ 12 etc. Are simple inequations.

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