1. Solving Inequalities Addition and Subtraction. Module 3, Lesson 3 Online Algebra VHS@PWCS

2. Inequalities Inequalities are statements that use the following symbols (the symbol points to the smaller quantity): > - Greater than < - Less than > - Greater than or equal to < - Less than or equal to ≠ - Not equal to

3. Graphing inequalities x > -1  Think of some values of x that fit this solution. How many values did you come up with? You should have come up with several.  Inequalities have an infinite number of solutions. In this case anything less than -1 is a solution.  Instead of points we use a line, to show that anything less than -1 is included.  We also use an open circle on -1 to show that numbers very close to -1 are included but not the -1 -6 -4 -2 0 2 4

4. Graph The Following Inequalities x > -2 Remember that we use an open circle and a line to graph this inequality. x > -2 Because this inequality represents x is greater than or equal to -2, -2 is part of the solution. To show this graphically we use a closed circle. -6 -4 -2 0 2 4

5. Solving Inequalities Solving inequalities are just like solving equations. c + -13 = 7 Recall that to solve this equation we add 13 to both sides. c + -13 + 13 = 7 + 13 c = 20 c + - 13 < 7 To solve this inequality. We do the same thing, add 13 to both sides. c + -13 + 13 < 7 + 13 c < 20 The only difference is the graph of the solution. 15 17 19 21 23 25

6. Solve and graph 4 > x - 12 1. Rewrite as addition. 4 > x + -12 2. Add 12 to both sides. 4 + 12 > x + -12 + 12 16 > x 3. If we flip the inequality it makes it easier to graph. x < 16 11 13 15 17 19 21 Notice that “point” is still pointing to the x, when we flip. This makes it easier to graph because if our x is on the left side of the inquality our line will go in the same direction as the symbol.

7. Solving Inequalities, A Recap  Solving inequalities is just like solving an equation.  To graph we use a line and either an open or closed circle.  Use an open circle with.  Use a closed circle with.