26 Solving Compound Inequalities - Bainbridge High …€¦ · 26 Solving Compound Inequalities...
Transcript of 26 Solving Compound Inequalities - Bainbridge High …€¦ · 26 Solving Compound Inequalities...
2.6 Notes Alg1.notebook October 09, 2012
Skills we've learned
Skills we need
5. 2(–6r – 5) < –3(4r + 2)4. 2y – 2 ≥ 2(y + 7)3. 4b + 4(1 – b) > b – 92. 5x – 9 ≤ 4.1x – 811. t < 5t + 24
Solve each inequality and graph the solutions.
1. x + 3 ≤ 10 23 < –2x + 3 2.3. 4x + 1 ≤ 25 4. 0 ≥ 3x + 3
26 Solving Compound Inequalities
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
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 .
Compound Inequality
2.6 Notes Alg1.notebook October 09, 2012
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.
II. Writing Compound Inequalities
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 October 09, 2012
And? Or?x < 10 and x > 0 x > 10 or x < 0
3. Solve the compound inequality and graph the solutions.
III. The Compound Inequality "And"
9 < x 10 < 5b.5 < x + 1 < 2a.
2.6 Notes Alg1.notebook October 09, 2012
IV. The Compound Inequality "Or"
4. Solve the compound inequality and graph the solutions.
8 + a > 7 OR 8 + a < 2a.
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
1
23
Does this triangle exist?
2
15
?
2.6 Notes Alg1.notebook October 09, 2012
Individual Quiz on Thursday!5 questions like "solve and graph 2x + 4 < 3(x 8)2 questions with an "and" or "or" problem3 story problems1 bonus
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
*31 + 4 problems
Quiz practice next slide
a.
b.
4. Write the compound inequality shown by the graph.
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 yearold 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.