Download Unit 22 GRE 501 Lesson Notes

GRE 501 LESSON/NOTES CRS SKILL GRE 501 Period____________ Name_________________________________________ LEVEL Level 1 – ALL students must attain mastery at this level DESCRIPTION GRE 301 Locate points on the number line R-­‐XEI 506 Solve first degree inequalities that don not require reversing the inequality sign Level 2 – MOST students will GRE 501 Identify the graph of a linear inequality on attain mastery of the focus skill in the number line isolation. Level 3 – SOME students will attain mastery of focus skill with other skills Level 4 – SOME students will attain mastery of focus topics covered in a more abstract way Level 5 – FEW students will GRE 602 Match number line graphs with solution sets attain mastery of the extension skill. VOCABULARY Inequality, The following symbols( <, ≤, >, ≥), Compound Inequality REQUIRED SKILL TO MASTER Inequalities on a number line Suggested Additional Practice Writing numerical inequalities, One-­‐step linear inequalities, Multi-­‐step linear inequalities, Using inequalities to describe real world contexts, Interpreting and solving linear inequalities, Compound inequalities Questions to be answered by the end of this lesson: 1. Which Properties of Inequalities differ from t he corresponding Properties of Equalities? Explain and include examples. 2. Why do the graphs of some inequalities include open circles, while others do not? Explain. 3. Describe two kinds of compound inequalities. 1 Level 1 1. Plot and label the following points on the number line below: a) 1
3
4
b) 4.5
c) 5
1
4
d) 0.75 2. Plot and label the following points on the number line below: a) 3 b) -­‐11 c)8 d)-­‐6 3. Solve each of the following inequalities: a) y − 3 ≤ −10
c) 8d < 24
b) n + 4 ≥ 9
d) c − 12 < −13
2 Level 2 x > x ≥ x < x ≤ Open Circle Solid Circle Open Circle Solid Circle Shade Right Shade Right Shade Left Shade Left 4. Write the inequality for each of the following. 3 5. Graph the following inequalities on the number lines provided. a. x > 2 b. x ≤ -­‐3 PROPERTIES OF INEQUALITY For all real numbers a, b, and c, where a ≤ b: Addition Property a + c ≤ b + c Subtraction Property a − c ≤ b − c Multiplication Property If c ≥ 0, then ac ≤ bc. If c ≤ 0, then ac ≥ bc. Division Property If c > 0, then . If c < 0, then . The only difference between solving an equation and solving an inequality is: “In an inequality if you multiply or divide by a negative number then you must flip the inequality.” Level 3 6. Which graph represents the solution of: x + 7 > 3? e.
. 4 7. Solve the inequality: 5x
+18 ≤ 3x − 4 . a. Is x = 2 a solutions to this inequality? b. Why or why not? 8. Solve the following inequalities:
a) 4(x + 3) > 32
b)
2
(x + 6) ≤ 5x − 22 3
Level 4 9. Frank owns and manages a Slinky company that sells each slinky for $6. The company must pay $2025 in fixed costs each month (utilities, payroll, etc.…) as well as pay $1.50 for the materials for each slinky they sell. Frank wants to find out how many Slinkys he needs to sell every month in order to break-­‐even or make a profit. He sets up the following inequality: 6s − (1.50s + 2025) ≥ 0 , such that b represents the number of Slinkys sold. a. How many Slinkys must he sell every month to break even? b. What if Frank wanted to find out how many Slinkys to make a profit of at least $1000? How would we need to change the inequality? 5 10. Michael’s test average in his mathematics class is 92, and his homework average is 81. The test average is 60% of the final grade, the quiz average is 15% of the final grade, and the homework average is 25% of the final grade. What quiz average does Michael need in order to have a final grade of at least 90? 11. Adrian works in New York City and makes $42 per hour. She works in an office and must get her suit dry cleaned everyday for $75. If she wants to make more than $260 a day, at least how many hours must she work? 12. Your brother has $2,000 saved for a vacation. His airplane ticket is $637. Write and solve an inequality to find out how much he can spend for everything else. Level 5 COMPOUND INEQUALITY A compound inequality is a pair of inequalities joined by and or or. 13. Match the inequalities with the sentence that best describes them. A. x ≤ 11 _______ x is less than 8 or x is greater than 11 B. x > 8 _______ x is less then 11 and x is greater than 8 C. x ≤ 8 _______ x is no more than 11 D. x < 8 or x > 11 _______ x is at most 8 E. 8 < x < 11 _______ x is greater than 8 6 14. Which inequality is represented by the graph below: -10
-5
0
5
10
a) − 4 ≤ x ≤ 3
b) − 4 < x ≤ 3
c) − 4 ≤ x < 3
d) − 4 ≤ x ≤ − 3
15.
Solve 2x + 1 ≥ 3 and 3x − 4 ≤ 17. Graph the solution. -4
-2
0
2
4
6
8
2
4
6
8
16.
Solve 5x + 1 > 21 or 3x +2 < -­‐1. Graph the solution -4
-2
0
7