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BEDMAS & Fractions
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Simple Trinomials as Products of Binomials
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Algebraic Expressions Containing Radicals 1
Addition Property of Equality
Three special types of lines
Quadratic Inequalities That Cannot Be Factored
Adding and Subtracting Fractions
Coordinate System
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Solving Quadratic Equations Using the Square Root Property
The Slope of a Line
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Arithmetic with Positive and Negative Numbers
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Powers and Roots of Complex Numbers
Adding, Subtracting and Finding Least Common Denominators
What the Factored Form of a Quadratic can tell you about the graph
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Solving Equations with Variables on Each Side
Finding the GCF of a Set of Monomials
Completing the Square
Solving Equations with Radicals and Exponents
Solving Systems of Equations By Substitution
Adding and Subtracting Rational Expressions
Laws of Exponents and Dividing Monomials
Factoring Special Quadratic Polynomials
Solving Quadratic Equations by Completing the Square
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Factoring Trinomials
Writing Decimals as Fractions
Using the Rules of Exponents
Evaluating the Quadratic Formula
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Multiplication by 429
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Introduction to Fractions
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Statements that express the inequality of algebraic expressions are called inequalities. The symbols that we use to express inequality are given below with their meanings.


Inequality Symbols

Symbol Meaning
< Is less than
Is less than or equal to
> Is greater than
Is greater than or equal to

It is clear that 5 is less than 10, but how do we compare -5 and -10? If we think of negative numbers as debts, we would say that -10 is the larger debt. However, in algebra the size of a number is determined only by its position on the number line. Fow two numbers a and b we say that a is less than b if and only if a is to the left of b on the number line. To compare -5 and -10, we locate each point on the number line (see figure below). Because -10 is to the left of -5 on the number line, we say that -10 is less than -5. In symbols,

-10 < -5.

We say that a is greater than b if and only if a is to the right of b on the number line. Thus we can also write

-5 > -10.

The statement a ≤ b is true if a is less than b or if a is equal to b. The statement a ≥ b is true if a is greater than b or if a equals b. For example, the statement 3 ≤ 5 is true, and so is the statement 5 ≤ 5.




Determine whether each statement is true or false.

a) -5 < 3

b) -9 > -6

c) -3 ≤ 2

d) 4 ≥ 4


a) The statement -5 < 3 is true because -5 is to the left of 3 on the number line. In fact, any negative number is less than any positive number.

b) The statement -9 > -6 is false because -9 lies to the left of -6.

c) The statement -3 ≤ 2 is true because -3 is less than 2.

d) The statement 4 ≥ 4 is true because 4 = 4 is true.


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