Inequations

# 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 inequatio**n 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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