2­6 Solving Compound Inequalities - Bainbridge Island School District

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 3. 4x + 1 25

2. 23 < ?2x + 3 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

October 09, 2012

And? x < 10 and x > 0

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

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