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20-Dec-2014Category

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- 1. Practice Problem

4a 7 17 AND 14 a > -5a + 3

Solve the Compound Inequality AND Graph

2. Practice Problem

Rachel is planning a wedding for 100 to 250 people, depending on costs. She has hired a caterer that charges $20 per person, plus a flat fee of $200.

Write an inequality in terms of p that describes how many people Rachel plans to invite.

Adjust the inequality to show how much the caterer will charge.

What is the range of catering fees that Rachel is considering.

3. Solving Absolute Value Equations & Inequalities

4. Absolute Value (of x)

Symbol lxl

The distance x is from 0 on the number line.

Always positive

Ex: l-3l=3

-4-3 -2-1 0 1 2

5. Ex:x= 5

What are the possible values of x?

x = 5orx = -5

6. To solve an absolute value equation:

ax+b= c, where c>0

To solve, set up 2 new equations, then solve each equation.

ax+b = corax+b = -c

** make sure the absolute value is by itself before you split to solve.

7. Ex: Solve6x-3= 15

6x-3 = 15or 6x-3 = -15

6x = 18or 6x = -12

x = 3orx = -2

* Plug in answers to check your solutions!

8. Ex: Solve2x + 7-3 = 8

Get the abs. value part by itself first!

2x+7= 11

Now split into 2 parts.

2x+7 = 11 or 2x+7 = -11

2x = 4 or 2x = -18

x = 2 or x = -9

Check the solutions.

9. Solving Absolute Value Inequalities

ax+b< c, where c > 0

Becomes an and problem

Changes to: c < ax+b < c

ax+b> c, where c > 0

Becomes an or problem

Changes to: ax+b > c or ax+b < -c

10. SOLVING ABSOLUTE-VALUE EQUATIONS AND INEQUALITIES

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ax b candax b c.

|ax b | c

|ax b | c

ax b candax b c.

When an absolute value is less than a number, the

inequalities are connected by and. When an absolute

ax b c orax b c.

|ax b | c

value is greater than a number, the inequalities are

connected by or.

ax b c orax b c.

|ax b | c

ax b c orax b c.

|ax b | c

11. Solving an Absolute Value Inequality

- Step 1:Rewrite the inequality as a conjunction or a disjunction.

12. If you have a < or you are working with a conjunction or an andstatement. Remember:Less thand

- If you have a > or you are working with a disjunction oran or statement.

Remember:Greator

- Step 2:In the second equation you must negate the right hand side and reversethe direction of the inequality sign.

13. Solve as a compound inequality.