Presentation on theme: "LESSON 6-3 COMPOUND INEQUALITIES"— Presentation transcript:
1 LESSON 6-3 COMPOUND INEQUALITIES Objective: To solve and graph inequalities containing “and” or “or”.
2 Real-World Connection Do you like to swim?Does your family have a swimming pool?Determining how to keep the water in a pool chemically balanced is one way this skill is used in real-world situations.
3 Vocabularycompound inequality – two inequalities joined by the word and or the word orsolution for and inequalities – (Intersection) any number that makes both inequalities truesolution for or inequalities – (Union) any number that makes either inequality true
4 STEPS for AND problemsWrite the compound inequality as two inequalities joined by and.Solve each inequality.Simplify and write the solutions as one statement.Graph the solution.
5 Translate the verbal phrase into an inequality Translate the verbal phrase into an inequality. Then graph the inequality.a.All real numbers that are greater than – 2and less than 3.Inequality:– 2 < x < 3Graph:b.All real numbers that are less than 0 or greater thanor equal to 2.x < 0 or x ≥ 2Inequality:Graph:
6 All real numbers that are less than –1 or greater than or equal to 4. c.Inequality:x < –1 or x ≥ 4d.All real numbers that are greater than or equalTo –3 and less than 5.Inequality:x ≥ –3 and x < 5= –3 ≤ x < 5
7 Write and graph a real-world inequality: CAMERA CARSA 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.
8 Write and graph a real-world inequality: SOLUTIONLet h represent 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.
9 You try… Solve each inequality and graph the solution. 1) -6 < 3x < 15 2) -3 < 2x-1 < 7
10 You try…3) 7 < -3a + 1 < 13Solution: -4 < n < -2
11 You try… 4) The books were priced between $3.50 and $6.00, inclusive. Solution: < b < 6
12 To solve OR problems, solve each inequality separately. 5) Solve –2x + 7 > 3 or 3x – 4 > 5.
13 You try…6) Write an inequality that represents all real numbers that are at most –5 or at least 3. Graph your solution.
14 Remember, when written like this, it is an AND problem! 7) Graph 3 < 2m – 1 < 9Remember, when written like this, it is an AND problem!3 < 2m – 1 AND 2m – 1 < 9Solve each inequality.Graph the intersection of 2 < m and m < 5.5-
15 Which inequalities describe the following graph? -2-1-3oy > -3 or y < -1y > -3 and y < -1y ≤ -3 or y ≥ -1y ≥ -3 and y ≤ -1Answer Now
16 Which is equivalent to -3 < y < 5? y > -3 or y < 5y > -3 and y < 5y < -3 or y > 5y < -3 and y > 5Answer Now
17 Which is equivalent to x > -5 and x ≤ 1? Answer Now
18 Summary Re-write the compound inequality into two problems and solve. For and problems, combine the solutions into one statement.For or problems, solve each separately.Graph.