2.6 Notes Alg1.notebook
October 09, 2012
2­6 Solving Compound Inequalities
Skills we've learned
Solve each inequality and graph the solutions.
1. t < 5t + 24
2. 5x – 9 ≤ 4.1x – 81
3. 4b + 4(1 – b) > b – 9
4. 2y – 2 ≥ 2(y + 7)
5. 2(–6r – 5) < –3(4r + 2)
Skills we need
1. x + 3 ≤ 10 2. 23 < –2x + 3 3. 4x + 1 ≤ 25 4. 0 ≥ 3x + 3
Warm­up Answers
2.6 Notes Alg1.notebook
October 09, 2012
2­6 Solving Compound Inequalities
Solve compound inequalities with one variable. Graph solution sets of compound inequalities with one variable.
A life guard can use compound inequalities to describe the safe pH levels in a swimming pool.
I. Vocabulary
Compound Inequality
The inequalities you have seen so far are simple inequalities. When two simple inequalities are combined into one statement by the words AND or OR, the result is called a compound inequality . 2.6 Notes Alg1.notebook
October 09, 2012
II. Writing Compound Inequalities
1. The free chlorine in a pool should be between 1.0 and 3.0 parts per million inclusive. Write a compound inequality to show the levels that are within this range. Graph the solutions. Let c be the chlorine level of the pool. 2. The pH level of a popular shampoo is between 6.0 and 6.5 inclusive. Write a compound inequality to show the pH levels of this shampoo. Graph the solutions. 2.6 Notes Alg1.notebook
And?
x < 10 and x > 0
October 09, 2012
Or?
x > 10 or x < 0
III. The Compound Inequality "And"
3. Solve the compound inequality and graph the solutions.
a. ­5 < x + 1 < 2
b. ­9 < x ­ 10 < ­5
2.6 Notes Alg1.notebook
October 09, 2012
IV. The Compound Inequality "Or" 4. Solve the compound inequality and graph the solutions. a. 8 + a > 7 OR 8 + a < 2
b. 4x < 20 OR 3x > 21
Shorthand notation can only be used for "and" problems, not "or"
Which is untrue?
7 < x < 5
­4 < x < ­1
2.6 Notes Alg1.notebook
October 09, 2012
V. Writing a Compound Inequality from a Graph
5. Write the compound inequality shown by the graph.
a.
b.
VI. Triangle Inequality
3
2
1
15
2
?
Does this triangle exist?
2.6 Notes Alg1.notebook
October 09, 2012
*31 + 4 problems
2­6 p. 138
#2, 4, 5, 9, 11, 12, 15 ­ 27 (x3), 28 ­ 38, 43, 45, 47 ­ 54
Triangle Inequality p.141 #1, 2, 4, 6
Individual Quiz on Thursday!
5 questions like "solve and graph 2x + 4 < 3(x ­ 8)
2 questions with an "and" or "or" problem
3 story problems Quiz practice next slide
1 bonus
Practice for your quiz:
1. Solve and graph 2x ­ 5 < 3(x + 4)
2. Solve and graph 6 ­ (5x ­ 1) > 3x ­ 8x + 9
3. The target heart rate during exercise for a 15 year­
old is between 154 and 174 beats per minute inclusive. Write a compound inequality to show the heart rates that are within the target range. Graph the solutions. 4. Write the compound inequality shown by the graph. a.
b.