1. Inequalities Review
BY:  Beverly Watola

2. Part 1: Writing and Graphing Inequalities
How are inequalities different than equations? An inequality is a mathematical sentence that compares expressions. 
An inequality uses the symbols ≤,  ≥, <, and > to compare quantities or amounts.
Example of equation:
5x + 3 = 28
Example of inequality: 
4x > 12

3. Part 1: Writing and Graphing Inequalities
Write the inequality for: Charlie has fewer than 5 candy canes. X < 5 Your Example: I have less than 200 math students. X < 200

4. Part 1: Writing and Graphing Inequalities
1.) Draw a circle on the number you are comparing. 
2.) Shade in the circle if your quantity could be equal to that number, or leave the circle empty if your quantity cannot be equal. 
3.) Draw an arrow and a line in the direction of all your possible solutions.
Example: 
Graph the inequality:  w is greater than to 7

5. Part 2: Steps to solving a one-step inequality
1.) Isolate the variable by performing the inverse operation. 
2.) Solve the inequality by doing the same thing to the other side of the inequality.  
Example :  
2m < -3
2     2
m < - 1.5

6. Part 3: One-Step Inequalities with negative coefficients
1.) Isolate the variable by performing the inverse operation. 
2.) Balance the inequality by doing the same thing to the other side of the inequality. 
3.) If you multiply or divide by a negative number, you must flip your inequality sign.  
Example : 
-9j > -18
-9    -9
 J <  2
           

7. Part 4: Solving and Graphing Two-Step Inequalities
1.) Isolate the variable on one side of the inequality sign, by eliminating the constant, then the coefficient. 
2.) Balance the inequality by doing same thing on both sides of the inequality sign. 
3.) If you divide or multiply by a negative number, you must flip your inequality sign. 
4.) Graph your solution on the number line by putting an open or closed circle on the answer, and drawing an arrow that points to all possible solutions. 
– m < 2
+ 10         < +10 
         4m < 12
           4      4
            m <  3

8. Good Luck on your Inequalities Unit Test!