Review Worksheet Chapter 3
Section 3-1 Linear Inequalities; Absolute ValueRules1.) You can add or subtract the same number to both sides of an inequalityIf a < b, then a + c < b + c2.) You can multiply or divide both sides of an inequality by the same positive number.If a < b and c > 0, then ac < bc3.) You can multiply or divide both sides of an inequality by the same negative number if you reverse the inequality sign.If a < b and c < 0, then ac > bcAbsolute Valuelxl = cSolution: x = c OR x = -clxl < cSolution: -c < x < clxl > cSolution: x < -c OR x > c
Problems:
1. (15-6X)/3 > 5
2. |x|<-8
3. |x-4|<3
4. |x-8|≥4
Section 3-2 Polynomial Inequalities in One Variable
Problems:
5. What are the 2 ways you can solve and graph a polynomial inequality with one variable?
6. (2x-1)(x+4)(x-3)2 ≥ 0
7. [(x-3)(x+6)] / [(x-1)(x-7)] ≥ 0
8. [(x+4)(x-3)2] / [(x+5)(x-2)] ≤ 0
Section 3-3 Polynomial Inequalities in Two Variablesy = mx + kAny point (x,y) ABOVE the line or parabola satisfies the inequality y > mx + kAny poiny (x,y) BELOW the line or parabola satisfies the inequality y < mx + k
Graph:
9. | y | > 1 10. y ≤ 2x-1
Section 3-4 Linear Programming The Corner Point Principle11. How many of each kind of TV should be produced to maximize the profit?
/Console
/Portable
/Total Hours
Machine A
/1
/3
/18
Machine B
/1
/1
/8
Machine C
/3
/1
/18
Profit per TV
/$70
/$40
/Answers:
1. x>0
2. no solution
3. 1<x<7
4. x=4x=12
5. sign analysis and graphing calculator
6. x≤-4 x≥ 1/2
7. x≤-6 1≤x≤3 x≥7
8. x≤-5 -4≤x≤2
9. 10.
11. 5 consoles 3 portables