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Linear Equations and Inequalitie
Solving Inequalities
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Graphing Equivalent Fractions Lesson Plan
Investigating Liner Equations Using Graphing Calculator
Graphically solving a System of two Linear Equatio
Shifting Reflecting Sketching Graph
Graphs of Rational Functions
Systems of Equations and Inequalities
Graphing Systems of Linear Equat
LINEAR FUNCTIONS: SLOPE, GRAPHS AND MODELS
Solving Inequalities with Absolute Values
Solving Inequalities
Solving Equations & Inequalities
Graph the rational function
Inequalities and Applications
Inequalities
Using MATLAB to Solve Linear Inequalities
Equations and Inequalities
Graph Linear Inequalities in Two Variables
Solving Equations & Inequalities
Teaching Inequalities:A Hypothetical Classroom Case
Graphing Linear Inequalities and Systems of Inequalities
Inequalities and Applications
Solving Inequalities
Quadratic Inequalities
Inequalities
Solving Systems of Linear Equations by Graphing
Systems of Equations and Inequalities
Graphing Linear Inequalities
Inequalities
Solving Inequalities
Solving Inequalities
Solving Equations Algebraically and Graphically
Graphing Linear Equations
Solving Linear Equations and Inequalities Practice Problems
Graphing Linear Inequalities
Equations and Inequalities
Solving Inequalities

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Solving Inequalities

Property of Comparisons
For all real numbers a and b, one and only one of the
following statements is true:
a < b, a = b, or a > b

Suppose you know two facts about the graphs of
three numbers a, b, and c.

1) The graph of a is to the left of the graph of b:
a < b

2) The graph of b is to the left of the graph of c:
b < c

From the graph above, you can see that the graph
of a is to the left of the graph of c: a < c

Transitive Property of Order
For all real numbers a, b, and c:

1) If a < b and b < c, then a < c.
2) If c > b and b > a, then c > a.

What happens when the same number is added
or subtracted to each side of an inequality?

3 6
3 6
3 + 4 _____ 6 + 4
3 - 4_____ 6 - 4
7 10
-12

Addition Property of Order
For all real numbers, a, b and c:

1) If a < b, then
2) If a > b, then a + c > b + c

What happens when the same number is
multiplied on each side of an inequality?
4 -3
4 -3
4(2) _____ -3(2)
4(-2)_____ -3(-2)
8 -6
-8 6

Multiplication Property of Order
For all real numbers a, b, and c such that

c > 0 (c is positive):	c < 0 (c is negative)
1) If a < b, then ac < bc
2) If a > b, then ac > bc

What would happen if we multiplied
both sides of an inequality by 0?

Example 1: Solve the inequality.

Example 2: Solve 6x - 3 < 7 + 4x and graph the
solution set.

Example 3: Solve 2(w - 8) + 9 ≥ 3(4 - w)- 4
and graph its solution set.

Example 4: Solve 4x > 4 (x + 2)
and graph its solution set.

Example 5: Solve y + 5 < 7y - 6(y - 1)
and graph its solution set.