GRAPHING SOLUTIONS Inequalities Inequality Symbols Symbol Meaning Less

GRAPHING SOLUTIONS Inequalities

Inequality Symbols Symbol Meaning < Less Than > Greater Than = Equal < Less Than or Equal To > Greater Than or Equal To

What You Need � A number line � A variable � To Shade � Shade ex: x, y, v, z, etc. ex: all solutions that make the inequality true! Do NOT shade the direction of the sign! Instead, only shade where the solutions are true.

x<5 � Step 1: Determine a solution that makes the inequality true. Does 5 work? Substitute 5 for the variable and check. � 5<5 This is false, so 5 does not work. � Does 6 work? Substitute 6 for the variable and check. � 6 < 5. This is false, so 6 does not work. � Does 4 work? Substitute 4 for the variable and check. � 4 < 5. This is true, so 4 does work ! � � Step 2: Draw a number line and the shade the side where all of the values make the inequality true. � 4 is a value that works & is located on the left of 5 on the number line. Shade on the left. 5

5>x � Step 1: Determine a solution that makes the inequality true. Does 5 work? Substitute 5 for the variable and check. � 5<5 This is false, so 5 does not work. � Does 6 work? Substitute 6 for the variable and check. � 5 > 6. This is false, so 6 does not work. � Does 4 work? Substitute 4 for the variable and check. � 5 > 4. This is true, so 4 does work ! � � Step 2: Draw a number line and the shade the side where all of the values make the inequality true. � 4 is a value that works & is located on the left of 5 on the number line. Shade on the left. 5

NOTICE!!! x < 5 has the same graph as 5 > x! Although the signs point in different directions, for these inequalities, the solutions that make the inequalities true are on the left of 5 on the number line.

AGAIN…. WARNING! Do NOT shade the direction of the sign! Instead, only shade the side where the solutions are true. > does not always mean shade on the right! < does not always means shade on the left!

x>5 � Step 1: Determine a solution that makes the inequality true. Does 5 work? Substitute 5 for the variable and check. � 5>5 This is false, so 5 does not work. � Does 4 work? Substitute 4 for the variable and check. � 4 > 5. This is false, so 4 does not work. � Does 6 work? Substitute 6 for the variable and check. � 6 > 5. This is true, so 6 does work ! � � Step 2: Draw a number line and the shade the side where all of the values make the inequality true. � 6 is a value that works & is located on the right of 5 on the number line. Shade on the right. 5

5<x � Step 1: Determine a solution that makes the inequality true. Does 5 work? Substitute 5 for the variable and check. � 5<5 This is false, so 5 does not work. � Does 4 work? Substitute 4 for the variable and check. � 5 < 4. This is false, so 4 does not work. � Does 6 work? Substitute 6 for the variable and check. � 5 < 6. This is true, so 6 does work ! � � Step 2: Draw a number line and the shade the side where all of the values make the inequality true. � 6 is a value that works & is located on the right of 5 on the number line. Shade on the right. 5

NOTICE!!! x > 5 has the same graph as 5 < x! Although the signs point in different directions, for these inequalities, the solutions that make it true are on the right of 5 on the number line.

AGAIN…. WARNING! Do NOT shade the direction of the sign! Instead, only shade the side where the solutions are true. > does not always mean shade on the right! < does not always means shade on the left!

x<5 � Step 1: Determine a solution that makes the inequality true. Does 5 work? Substitute 5 for the variable and check. � 5<5 This is true, so 5 does work. � Does 6 work? Substitute 6 for the variable and check. � 6 < 5. This is false, so 6 does not work. � Does 4 work? Substitute 4 for the variable and check. � 4 < 5. This is true, so 4 does work ! � � Step 2: Draw a number line and the shade where all of the values make the inequality true. Also shade the circle, as the solution can also be 5! � 4 is a value that works & is located on the left of 5 on the number line. Shade on the left. 5

5>x � Step 1: Determine a solution that makes the inequality true. Does 5 work? Substitute 5 for the variable and check. � 5>5 This is true, so 5 does work. � Does 6 work? Substitute 6 for the variable and check. � 5 > 6. This is false, so 6 does not work. � Does 4 work? Substitute 4 for the variable and check. � 5 > 4. This is true, so 4 does work ! � � Step 2: Draw a number line and the shade the side where all of the values make the inequality true. Also shade the circle, as the solution can also be 5! � 4 is a value that works & is located on the left of 5 on the number line. Shade on the left. 5

NOTICE!!! x < 5 has the same graph as 5 > x! Although the signs point in different directions, for these inequalities, the solutions that make it true are on the left of 5 on the number line.

AGAIN…. WARNING! Do NOT shade the direction of the sign! Instead, only shade the side where the solutions are true. > does not always mean shade on the right! < does not always means shade on the left!

x>5 � Step 1: Determine a solution that makes the inequality true. Does 5 work? Substitute 5 for the variable and check. � 5>5 This is true, so 5 does work. � Does 4 work? Substitute 4 for the variable and check. � 4 > 5. This is false, so 4 does not work. � Does 6 work? Substitute 6 for the variable and check. � 6 > 5. This is true, so 6 does work ! � � Step 2: Draw a number line and the shade the side where all of the values make the inequality true. Also shade the circle, as the solution can also be 5! � 6 is a value that works & is located on the right of 5 on the number line. Shade on the right. 5

5<x � Step 1: Determine a solution that makes the inequality true. Does 5 work? Substitute 5 for the variable and check. � 5<5 This is true, so 5 does work. � Does 4 work? Substitute 4 for the variable and check. � 5 < 4. This is false, so 4 does not work. � Does 6 work? Substitute 6 for the variable and check. � 5 < 6. This is true, so 6 does work ! � � Step 2: Draw a number line and the shade the side where all of the values make the inequality true. Also shade the circle, as the solution can also be 5! � 6 is a value that works & is located on the right of 5 on the number line. Shade on the right. 5

NOTICE!!! x > 5 has the same graph as 5 < x! Although the signs point in different directions, for these inequalities, the solutions that make it true are on the right of 5 on the number line.

AGAIN…. WARNING! Do NOT shade the direction of the sign! Instead, only shade the side where the solutions are true. > does not always mean shade on the right! < does not always means shade on the left!

When do I shade the circle? OPEN CIRCLE CLOSED CIRCLE < > =

Practice: Does the solution work? 1. 4 + 1 = 5 yes x + 1 = 5 for x = 4 _________ 13 - 2 ≠ 10 no 2. 13 - w = 10 for w = 2 ________ 3. 2 ∙ 10 ≠ 12 no 2 • v = 12 for v = 10 _________ 4. 14 ÷ 7 = 2 yes 14 ÷ p = 2 for p = 7 _________

Graph each inequality 1. w 0 0 2. b 4 -4 3. j>5 5 4. 6>q 6