Inequations

An inequation is an algebraic inequality:

x + 3y < 7

The variables that appear in these inequalities are also called unknowns. The degree of an inequation is the biggest degree of its unknowns.

A solution of an inequation is a value that makes the inequality true. The solution of an inequation is the set of all the solutions.

x = 7 is a solution of x + 3 > 0, and (-3,∞) is the solution of this inequation.

Two inequations are equivalent if they have the same solution. To obtain an equivalent inequation we can do only two basic operations:
 
–Add or subtract the same expression in both sides of the inequation.

               x + 3  > 0       x + 3 – 3 > 0 – 3       x > -3

–Multiply or divide by the same number (except zero) in both sides of the inequation. If the number is negative we have to change the direction of the inequality.

          -x ≤ 7          x ≥ -7

           2x < -8       x < -4

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