Algebra Honors (Period 6 & 7)

Inequalities in One Variable
Solving Problems Involving  Inequalities 10-3

For practice, we went through the examples in our textbook on Page 469
We discovered that reading and re-reading the problem was critical to make sure we answered the exact question.  As noted in Example 1: the question asked what is the minimum total distance, to the nearest mile, that she will have to travel...?"  The critical part, was "to the nearest mile."  Please read the problem and then realize  why re arrived at the following:
Let d = the distance fro the sign to home
d - 16 > 25
solving that open sentence we get
d > 41
Since the distance needs to be greater than 41, the next whole number is 42 so the answer is
The minimum distance she will travel is 42 miles.

To translate phrases such as "is at least" and "is no less than"  you will need   ≥ 
...think I want at least $200 when going to Disneyland. I obviously want more.. but I will be happy with $200.

To translate phrases such as "is at most" and "is no more than"  you will need   ≤
...think I want at most 7 problems of homework. I really want fewer than 7 but I'll be okay with 7.

Algebra Period 3

Using Equations that Factor 6-9

Word Problems

Problem Solving Guidelines

Phase 1: Understanding the problem
Ask yourself:

What am I trying to find?
What data am I given?
Have I ever solved a similar problem?

Phase 2: Develop and carryout a PLAN

Ask yourself:

What strategies might I use to solve the problem?
How can I correctly carry out the strategies I selected?

Phase 3: Find the ANSWER and CHECK

Ask Yourself:

Does the proposed solution check?
What is the answer to the problem?
Does the answer seem reasonable?
Have a stated the answer clearly? ( labeled??)


Practice translating some of these word problems:

The product of one more than a number and one less than the number is 8.
Find the number.

Start with a let statement. It can be as simple as
Let x = the number.

the product... means it will be a multiplication problem
one more than a number x + 1
one less than the number x - 1

so (x +1)(x- 1) = 8

in order to solve you must use FOIL or the box method
but just looking at ( x + 1) (x -1) you know that is the difference of 2 squares... so
x² - 1 = 8 move the eight to the other side setting the equation equal to 0

x² - 9 = 0 and now it is also the difference of two squares or
(x-3)(x+3) = 0

so x - 3 = 0 and x + 3 = 0 so x = + 3 OR x = -3



The square of a number minus twice the number is 48. Find the number

Let x = the number

the square of a number x²
minus twice the number -2x

so x² -2x = 48

again it becones x² -2x - 48 = 0

factor and you get (x -8)(x+6) = 0 Using the principle of Zero products
x = 8 or x = -6