1. What are the following properties?
Bell Work
What are the following properties?
1) x + 9 = 9 + x
2) ( x + 3 ) = 2x + 6 3)

2. Evaluating Algebraic Expressions
Examples
1) Evaluate the expression 3y + 2y when 5 = y
Step 1
substitute (plug in) 5 for the variable y
3(5) + 2(5)
Step 2
Solve
= 25

3. 2) Evaluate the expression2x^3 – x^2 + y for x = 3 and y = –2
Step 1
Substitute (plug it in plug it in)
2(3)^3 – (3)^2 + (-2)
Step 2
Solve
=2(27) (-2)
= (-2)
=43

5. Let x = 10, y = 4, z = 2, and evaluate the following.

6. Answers
1) 22
2) 14
3) 4

7. (3.6) Open Sentences and Solution Sets
Every sentence that contains a variable is called a open sentence (an open sentence is neither true nor false)
examples
x + 6 =9
3y = 12
2n>0

8. The numbers from the domain that make the sentence true are the elements of the solution set (can contain one or more numbers at times or no numbers at all)
Example
using the domain (0,1,2,3) find the solution set of the open sentence
Solution
Substitute the numbers from above for x

9. Let x = 0
0 + 6 = 9 is false
let x = 1
1 + 6 = 9 is false
Which of the numbers in the domain is true? Keep plugging in the numbers until you find the answer

10. Answer
Solution set (3) because = 9
Try another one
Using the domain (0,1,2,3) find the solution set of the open sentence 2n > 0
Remember just plug in the numbers one at a time from the domain to find out which ones make the expression 2n > 0 true

11. Answer: solution set = (1,2,3) because
2(1) > > 0
n=2
2(2) > > 0
n=3
2(3) > > 0