3. Inequalities: Theory

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The line below is a number line and extends to infinity in both directions. All real numbers (pos and neg) are represented by a point on the line.

Picking a number, x, all values to the right of x are greater than x, like wise in reverse for the left.

The identity {x: x > 3} is read: let x be the set of all numbers greater than 3. This can be represented on a number line:

The open circle denotes that x is greater but not equal to 3. This form applies to greater and less than. Greater than or equal is represented by a filled in circle. Identities can have two boundaries, these are called quadratic inequalities.

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Axioms of inequalities. Simplifying inequalities simply means re-arranging a complicated inequality such as 6x + 8 - 2 > 4x + 1 into the form x > some number.

Modulus just means the magnitude, regardless of negative or positive. More understanding will be had in how to answer every type of question.

REMEMBER, MULTIPLYING BOTH SIDES BY -1 REVERSES THE SYMBOLS