Writing Inequalities x is less than 7 x is greater than 5 This is really easy. x is less than 7 x is greater than 5 x is less than or equal to –2 x is greater than or equal to 13 The sum of x and 4 is greater than 11 2 is less than or equal to x is less than 9

Identifying Solutions of Inequalities by Evaluating Determine if the numbers given are solutions to the given inequalities. a) 2 a) 3 a) 1 No No Yes b) 4 b) -1 b) -3 No Yes No c) -3 c) -2 c) 0 Yes Yes No

Graphs of Inequalities Graph the following inequalities. -4 -2 0 2 4 6 8 -4 -2 0 2 4 6 8 -4 -2 0 2 4 6 8 0 2 4 6 8 10 12 -14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12

More Graphs of Inequalities Write an inequality for each graph. 0 2 4 6 8 10 12 -1 1 3 5 7 9 11 4 6 8 10 12 14 16 -8 -6 -4 -2 0 2 4 -10 -8 -6 -4 -2 0 2 0 2 4 6 8 10 12

Solving Inequalities Solving Inequalities with variables is just like regular equations that have variables. The main difference is that a regular equation with a variable has only one answer, and an inequality with a variable has a range of answers. Regular Equation Inequality x - 4 = 3 x - 4 > 3 Let’s graph this answer on a number line. + 4 + 4 + 4 + 4 x = 7 x > 7 5 7 9 11 13 15 17 Notice the bold section of the line and that the circle on the seven is open. The answer is one distinct number The answer is the range of numbers greater than seven

Solving One-Step Inequalities Using Addition & Subtraction 10 12 14 16 18 20 22 -16 -14 -12 -10 -8 -6 -4 -4 -2 0 2 4 6 8 That was easy 0 2 4 6 8 10 12 0 2 4 6 8 10 12

More One-Step Inequalities Using Addition & Subtraction -16 -14 -12 -10 -8 -6 -4 That was easy -1 1 3 5 7 9 11 4 6 8 10 12 14 16

Solving One-Step Inequalities Using Multiplication & Division 19 21 23 25 27 29 -16 -14 -12 -10 Asi de Facil -16 -14 -12 -10 -8 -6 -4 2 4 6 8

Dividing Inequalities by a Negative 0 2 4 6 8 10 12 -8 -6 -4 -2 0 2 4 0 2 4 6 8 10 12 Asi De Facil -4 -2 0 2 4 6 8

More Dividing Inequalities by a Negative -12 -10 -8 -6 -4 -2 0 3 5 7 9 11 13 15 0 2 4 6 8 10 12 Asi De Facil -4 -2 0 2 4 6 8

Even Numbers Only for All Homework Page 168: 12 – 16 & 22 - 34 Page 174: 14 – 28 Page 181: 12 – 26 Even Numbers Only for All

Solving Multi-Step Inequalities 1 3 5 12 14 16 -16 -14 -12 -10 -8 -6 -4 That was easy

More Multi-Step Inequalities -1 1 3 6 8 10 That was easy

Even More Multi-Step Inequalities 1 3 5 -10 -8 -6 Asi de Facil

Homework Page 190: 10 - 28 Even Numbers