This would be read as the solution set is all numbers greater than or equal to negative 5. Solution Sets

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Carmel Bailey
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1 .notebook Solution Sets A solution to an inequality is NOT a single number. It will have more than one value This would be read as the solution set is all numbers greater than or equal to negative 5. Solution Sets Let's name the numbers that are solutions of the given inequality. r > 10 Which of the following are solutions? {5, 10, 15, 20} 5 > 10 is not true So, not a solution 10 > 10 is not true So, not a solution 15 > 10 is true So, 15 is a solution 20 > 10 is true So, 20 is a solution Answer: {15, 20} are solutions of the inequality r > 10 Solution Sets 1

2 .notebook Let's try another one. ; {3, 4, 5, 6, 7, 8} 30 (4)3 30 (4) (4) click to reveal click to reveal click to reveal 30 (4) click to reveal 30 (4) click to reveal 30 (4) click to reveal Solution Sets The Circle An open circle on a number shows that the number is not part of the solution. It is used with "greater than" and "less than". The word equal is not included. < > A closed circle on a number shows that the number is part of the solution. It is used with "greater than or equal to" and "less than or equal to". < > 2

3 .notebook The Arrow If the variable is on the left, the arrow points in the direction of those numbers who satisfy the inequality. *If the variable is on the left side of the inequality, then < and will show an arrow pointing left. *If the variable is on the left side of the inequality, then > and will show an arrow pointing right. Notice that < and look like an arrow pointing left and that > and look like an arrow pointing right. But what if the variable isn't on the left? Do the opposite of where the inequality symbol points. Jul 29 5:11 PM 3

4 .notebook What is the number in the inequality? What kind of circle should be used? In what direction does the line go? x is less than 5 Step 1: Rewrite this as x < 5. Step 2: What kind of circle? Because it is less than, it does not include the number 5 and so it is an open circle. 4

5 .notebook x < 5 Step 3: Draw an arrow on the number line showing all possible solutions. Numbers greater than the variable, go to the right. Numbers less than the variable, go to the left. Step 4: Draw a line, thicker than the horizontal line, from the dot to the arrow. This represents all of the numbers that fulfill the inequality. x is less than or equal to 5 Step 1: Rewrite this as x 5. Step 2: What kind of circle? Because it is less than or equal to, it does include the number 5 and so it is a closed circle. 5

This represents all of the numbers that fulfill the inequality.

6 .notebook x 5 Step 3: Draw an arrow on the number line showing all possible solutions. Numbers greater than the variable, go to the right. Numbers less than the variable, go to the left. Step 4: Draw a line, thicker than the horizontal line, from the dot to the arrow. This represents all of the numbers that fulfill the inequality. You try Graph the inequality x > click 2 on the number line for answer Graph the inequality 3 > x click 3 on the number line for answer 6

7 .notebook Try these. Graph the inequalities. 1. x > 3 2. x < 4 Try these

8 .notebook 1 This solution set would be x > 4. True False False 2 A x > 3 B x < 3 C x < 3 D x > 3 D 8

9 .notebook 3 A B C D < x > x 11 > x 11 < x A 4 A x > 1 B x < 1 C x < 1 D x > 1 C 9

10 .notebook 5 A 4 < x B C 4 > x 4 < x C D 4 > x 6 A x > 0 B x < 0 C x < 0 D x > 0 B 10

11 .notebook Nov 28 2:49 AM 11

Notes Lesson 3 4. Positive. Coordinate. lines in the plane can be written in standard form. Horizontal

Notes Lesson 3 4. Positive. Coordinate. lines in the plane can be written in standard form. Horizontal A, B, C are Notes Lesson 3 4 Standard Form of an Equation: Integers Ax + By = C Sometimes it is preferred that A is Positive All lines in the plane can be written in standard form. Oblique Coordinate Horizontal