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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

Properties of Inequalities For all real numbers a, b, c:

Rule 1	If a < b, then b > a
Rule 2	If a < b, then -a > -b
Rule 3	If a < b, then for all real numbers c, a + c < b + c
Rule 4	If a < b, then for all POSITIVE c, ac < bc
Rule 5	If a < b, then for all NEGATIVE c, ac > bc

Solution sets to a linear inequality can be shown using table 2.6(pg 174)

Steps to Solving a Linear Inequality
(The < sign here could be ANY inequality.)

1. Eliminate fractions by multiplying both sides by the least common denominator. KEEP THE LCM POSITIVE!

2. Remove grouping symbols using the distributive property

3. Simplify each side by combining like terms. (ax + b < cx + d)

4. Use addition property of equality to isolate the variable. (gx + b) < d

5. Use addition property of equality to isolate the constant term. to get the
equation into the form (gx < h).

6. If g > 0, use the multiplication property of equality to solve for x (x < k).

7. If g < 0 use the multiplication property of equality to solve for x and CHANGE the direction of the inequality.

8. Check your solution in the original inequality by substitution.