Download Inequalities - Garnet Valley School District

Algebra III Academic
Unit I: Equations, Inequalities, and Mathematical Modeling
Goal
 Represent solutions of linear inequalities in one variable
 Use properties of inequalities to create equivalent inequalities
 Solve linear, polynomial and rational inequalities in one variable
 Solve absolute value inequalities
 Use inequalities to model and solve real-life problems
Key Vocabulary
 Absolute Value Equation
 Inequality
 Absolute Value Inequality
 Intercepts
 Complex Number
 Interval
 Compound Interest
 Key Numbers
 Conjugate
 Linear Forms
 Discriminant
 Mathematical Model
 Domain
 Polynomial Equation
 Double Inequality
 Polynomial Inequality
 Function
 Properties of Inequalities
 Identity
 Radical Equation
 Imaginary Number
 Rational Equation
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Rational Inequality
Range
Slope
Solution
Symmetry
Standard Form of a Circle
Standard Form of a Complex
Number
Test Intervals
Lesson 5: Inequalities
Multiple Solutions –
Equations:
1
Solve 3( x  7)  18  (9 x  9)
3
Inequalities – Another way to get multiple answers is to look for numbers that make one side bigger or smaller
than the other side.
Solving Inequalities
1. Simplify each side separately.
2. Get all variables on one side…good idea to get variable on the left side
Graph the numbers described by the inequalities that follow. Write your answers in interval notation.
x > -2
4 y
5(3 – t) < 7 – t
1
2m £ - (-6 - 4m)
2
Compound Inequalities
Solve, graph and write your solution in interval notation.
3
 4  m  7  7
-3 £ 6x -1< 3
4
1£ 2x + 7 <11
Four (4) Cases in Absolute Value Inequality
Case 1 :
x < a or x £ a
Case 2:
x > a or x ³ a
Case 3:
x < -a or x £ -a

The absolute value of any number is either zero (0)
or positive which can never be less than or equal to a negative number.

The answer for this case is always no solution.
Case 4:
x ³ -a or x ³ -a

The absolute value of any number is either zero (0)
or positive. It makes sense that it must always be greater than any negative
number.
numbers.

The answer for this case is always all real
or
Solve.
3x + 2 - 4 = 4
3- 2x < 5
2x -1 + 3 ³ 8
II. Word Problems
Word problems involving inequalities are often written and solved as equations, then it is determined
whether the set of answers is above or below the one that makes it equal. This only allows you to solve
problems in which you know how changing one value will affect every other one in the problem.
Write the phrases using inequality notation:
a) x is at least n ____________________
b) x is between a and b _____________________
c) x is no greater than n _____________
d) x is at most m __________________________
e) x is no less than __________________
f) x is between a and b inclusive _____________
Find all sets of 4 consecutive integers whose sum is between 10 and 20.
You are considering two job offers. The first job pays $3000 per month. The second job pays $1000 per
month plus a commission of 4% of your gross sales. How much must you earn in gross sales for the second
job to pay more than the first job.
Find the domain:
x-5
3- 4x
5x - 8
Polynomial Inequalities
x2 - x < 6
x 2 - x ³ 20
4x 2 - 5x - 6 > 0
Assignment: Page 137, 5-57 every other odd
Rational Inequalities
2x - 7
£3
x-5
x-2
³ -3
x -3
4x -1
>3
x-6
Assignment: Page 137, 5-57 every other odd, 97-105 odd, Page 147, 13-17 odd, 39-43 odd,