Writing Inequalities Your age is LESS THAN 19 years. Your height is GREATER THAN 52 inches. Your speed is LESS THAN OR EQUAL TO 62. There are GREATER THAN OR EQUAL TO 42 stinkbugs. a < 19 under below fewer than h > 52 more than over exceeds no more than maximum at most no less than minimum at least s 62 ≤ s 42 ≥ VOCABULARY above beneath

Graph 1.Draw a number line with 19 in the middle. 2.Next, draw an open circle around Now think: Could a = 19? …(you should be thinking)… * a cannot be 19 – Why? is not less than 19. * Since a ≠ 19, leave the circle open. 4.Finally, draw the arrow. Graphing Inequalities “less than” “greater than”

Graph Graphing Inequalities 1.Draw a number line with 10 in the middle. 2.Next, draw an open circle around Now think: Could x = 10? …(you should be thinking)… * x cannot be 10 – Why? 10 is not greater than 10. * Since x ≠ 10, leave the circle open. 4.Finally, draw the arrow. “less than” “greater than”

Graphing Inequalities Graph 1.Draw a number line with 62 in the middle. 2.Next, draw an open circle around Now think: Could s = 62? * s can be 62 – Why? ––> s is less than or equal to 62 * Since s could = 62, close the circle 4.Finally, draw the arrow. “less than” “greater than”

Graph Graphing Inequalities 1.Draw a number line with 42 in the middle. 2.Next, draw an open circle around Now think: Could x = 42? * x can be 42 – Why? * Since x could = 42, close the circle ––> x is greater than or equal to 42 4.Finally, draw the arrow. “less than” “greater than”

Evaluating Inequalities 1. –15 ≥ 7 – 11x In this inequality, could x = 3? Rewrite the inequality, but substitute 3 for x. –15 ≥ 7 – 11x 3 Simplify the variable side. –15 ≥ 7 – 33 –15 ≥ –26 “Negative fifteen is greater than, or equal to, negative 26.” Now, read it...is that true? < 7 In this inequality, could: x = 6x = –6x = 30 a. x = 6? b. x = –6?c. x = 30? –2 7 “Seven is less than seven?” ANSWER: not 6 is not a possible value for x. 11 ANSWER: not –6 is not a possible value for x. –1 ANSWER: is 30 is a possible value for x. 2

Evaluating Inequalities 3(3) + 4 > −5 \ / > −5 \ / 13 > −5 Read it. Is that true? TRUE -- x could = 3. 3(−3) + 4 > −5 \ / −9 + 4 > −5 \ / –5 > −5 Read it. Is that true? FALSE -- x could not = –3. 7 \/ - 7 \ / 5 ≤ 5 TRUE – x could be 7 – ≤ 5 FALSE – x could NOT be –7

Inequalities – Multiplying w/ Negatives Solve 1.Look at the constant attached to the variable. 2.Now, divide both sides by –9. If the number attached to the variable is negative, you’ve got to flip the inequality.

1.Look at the constant attached to the variable. –5 2.Now, multiply both sides by –5. If the number attached to the variable is negative, you’ve got to flip the inequality. Solve –3 Inequalities – Dividing w/ Negatives Is it negative?

Solving Inequalities b > – ≤ 23 + a 3. –19 – x ≥ –3 4. – The product of a number and two, less than fifteen, is at least thirty–five 10. The quotient of a number and two decreased by three is no more than eleven. no flip –9 ≤ ax ≥ –16b > –19 no flip flip no flip flip no flip flip –11 < y–18 ≤ by < –72 x ≤ 24z > –24 15 – 2x ≥ 35 x – 3 ≤ 11 2 x ≤ –10x ≤ 28 flipno flip