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Warm-up

Warm-up. Use the numbers: -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5 Which numbers are less than or equal to -1 and greater than or equal to -2? Which numbers are greater than 1 or less than -3? Which numbers are less than or equal to -2 and less than or equal to 2?

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Warm-up

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  1. Warm-up • Use the numbers: -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5 • Which numbers are less than or equal to -1 and greater than or equal to -2? • Which numbers are greater than 1 or less than -3? • Which numbers are less than or equal to -2 and less than or equal to 2? • Which numbers are greater than -1 or greater than 3? -2, -1 -5, -4, 2, 3, 4, 5 -5, -4, -3, -2 0, 1, 2, 3, 4, 5

  2. w – 6 ANSWER p>– 9 2. – 5 ANSWER W 30 > < – – Daily Homework Quiz For use after Lesson 6.2 Solve the inequality. Graph your solution. 1. – 72 < 8p

  3. a. All real numbers that are greater than –2and less than 3. Graph: b. All real numbers that are less than 0or greater than or equal to 2. Graph: EXAMPLE 1 Write and graph compound inequalities Translate the verbal phrase into an inequality. Then graph the inequality. Inequality: – 2 < x < 3 x < 0 or x ≥ 2 Inequality:

  4. 1. All real numbers that are less than –1or greater than or equal to 4. All real numbers that are greater than orequal To –3and less than 5. 2. GUIDED PRACTICE Example 1 Inequality: x < –1 or x ≥ 4 = –3 ≤ x < 5 Inequality: x ≥ –3andx < 5

  5. EXAMPLE 2 Write and graph a real-world compound inequality CAMERA CARS A crane sits on top of a camera car and faces toward the front. The crane’s maximum height and minimum height above the ground are shown. Write and graph a compound inequality that describes the possible heights of the crane.

  6. EXAMPLE 2 Write and graph a real-world compound inequality SOLUTION Let hrepresent the height (in feet) of the crane. All possible heights are greater than or equal to 4 feet and less than or equal to 18 feet. So, the inequality is 4 ≤ h ≤ 18.

  7. Solve a compound inequality with and Solve 2 < x + 5 < 9.Graph your solution. SOLUTION Separate the compound inequality into two inequalities. Then solve each inequality separately. 2 < x + 5 x + 5 < 9 and Write two inequalities. 2 – 5< x + 5 – 5 and x + 5 – 5< 9 – 5 Subtract 5 from each side. and x < 4 –3 < x Simplify. The compound inequality can be written as – 3 < x < 4.

  8. Graph: EXAMPLE 3 Solve a compound inequality with and ANSWER The solutions are all real numbers greater than –3and less than 4.

  9. An investor buys shares of a stock and will sell them if the change c in value from the purchase price of a share is less than –$3.00 or greater than $4.50. Write and graph a compound inequality that describes the changes in value for which the shares will be sold. 3. for Example 2 and 3 GUIDED PRCTICE Investing SOLUTION Let c represent the change in the value from the purchase price of the shares where all possible changes are less than –$3.00 or greater than $4.50.

  10. for Example 2 and 3 ANSWER So the inequality is c < –3 or c > 4.5.

  11. 4. –7 < x – 5 < 4 EXAMPLE 3 Solve a compound inequality with and Solve the inequality. Graph your solution. SOLUTION Separate the compound inequality into two inequalities. Then solve each inequality separately. –7 < x – 5 x – 5 < 4 and Write two inequalities. –7 + 5< x –5 + 5 x – 5 + 5< 4 + 5 and Add 5 to each side. and –2 < x x < 9 Simplify. The compound inequality can be written as – 2 < x < 9.

  12. 9 Graph: – 6 – 4 – 2 0 2 4 6 8 10 EXAMPLE 3 for Example 2 and 3 ANSWER The solutions are all real numbers greater than –2 and less than 9.

  13. 5. 10 ≤ 2y + 4 ≤ 24 for Example 2 and 3 GUIDED PRACTICE Solve the inequality. Graph your solution. SOLUTION Separate the compound inequality into two inequalities. Then solve each inequality separately. 2y + 4 ≤ 24 10 ≤ 2y + 4 and Write two inequalities. 10 – 4≤ 2y + 4 – 4 and 2y + 4 – 4 ≤ 24 – 4 Subtract 4 from each side. 6 ≤ 2y and 2y ≤ 20 Simplify. 3 ≤ y y ≤ 10 and The compound inequality can be written as 3 ≤ y ≤ 10.

  14. 3 Graph: 0 2 4 6 8 10 12 EXAMPLE 3 Solve a compound inequality with and ANSWER The solutions are all real numbers greater than or equal to 3 andless than or equal to 10.

  15. 6. –7< –z – 1< 3 Solve a compound inequality with and Solve the inequality. Graph your solution. SOLUTION Separate the compound inequality into two inequalities. Then solve each inequality separately. and –z – 1 < 3 –7 < –z – 1 Write two inequalities. –7 + 1< –z – 1 + 1 and –z– 1 + 1 < 3 + 1 Add 1 to each side. Simplify. 6 < z and z > – 4 The compound inequality can be written as – 4 < z < 6.

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