Post on 18-Dec-2015
LESSON 6-3LESSON 6-3COMPOUND COMPOUND INEQUALITIESINEQUALITIESObjective: To solve and graph inequalities containing “and” or “or”.
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.
Vocabulary
compound inequality – two inequalities joined by the word and or the word or
solution for and inequalities – (Intersection) any number that makes both inequalities true
solution for or inequalities – (Union) any number that makes either inequality true
STEPS for AND problems
1. Write the compound inequality as two inequalities joined by and.
2. Solve each inequality.3. Simplify and write the solutions as
one statement.4. Graph the solution.
Translate the verbal phrase into Translate the verbal phrase into an inequality. Then graph the an inequality. Then graph the inequality.inequality.a. All real numbers that are greater than – 2 and less than 3.
Inequality:
Graph:
b.All real numbers that are less than 0 or greater thanor equal to 2.
Inequality:
Graph:
– 2 < x < 3
x < 0 or x ≥ 2
d. All real numbers that are greater than or equal To –3 and less than 5.Inequality:
All real numbers that are less than –1 or greater thanor equal to 4.
c.
Inequality:
= –3 ≤ x < 5 x ≥ –3 and x < 5
x < –1 or x ≥ 4
Write and graph a real-world inequality:
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.
CAMERA CARSCAMERA CARS
Let 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.
SOLUTIONSOLUTION
Write and graph a real-world inequality:
You try…
Solve each inequality and graph the solution.
1) -6 < 3x < 15 2) -3 < 2x-1 < 7
You try…
3) 7 < -3a + 1 < 13
Solution: -4 < n < -2
You try…
4) The books were priced between $3.50 and $6.00, inclusive.
Solution: 3.50 < b < 6
To solve OR problems, solve each inequality separately.5) Solve –2x + 7 > 3 or 3x – 4 > 5.
You try…
6) Write an inequality that represents all real numbers that are at most –5 or at least 3. Graph your solution.
7) Graph 3 < 2m – 1 < 9
Remember, 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.
0 5-5
Which inequalities describe the following graph?
1. y > -3 or y < -12. y > -3 and y < -13. y ≤ -3 or y ≥ -14. y ≥ -3 and y ≤ -1
-2 -1-3oo
Answer NowAnswer Now
Which is equivalent to-3 < y < 5?
1. y > -3 or y < 52. y > -3 and y < 53. y < -3 or y > 54. y < -3 and y > 5
Answer NowAnswer Now
Which is equivalent to x > -5 and x ≤ 1?
1. -5 < x ≤ 12. -5 > x ≥ 13. -5 > x ≤ 14. -5 < x ≥ 1
Answer NowAnswer Now
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.
Homework:
Study for quiz Wednesday, 1/15
Quiz covers chapter 6 sections 1-3
Exit Ticket
Explain the difference between “and” vs. “or” compound inequalities.
How do you solve a compound inequality?