1. OTCQ Simplify 6÷ 2(3) + (1 - 32) 2 1 12 98

2. Aim 1-3 How do we define open sentences?
NY AA 21, AA 22, AA 24
Homework Read Section 1-3 do problems 18 – 26 on page 14

3. Objectives The student will be able to:
Define vocabulary of algebra
Solve open sentences by performing arithmetic operations.

4. A Variable Expression is a group of numbers, variables, and operations
A Variable Expression is a group of numbers, variables, and operations. (No equal sign)
Examples
12m - 42
3x + 2

5. An Equation is a mathematical sentence that contains an equal sign (=).
Examples
2 + 4 = 6
3x + 2 = 11

6. A sentence that has the symbol ,  , , or  is called an inequality.
Examples
3a  43
x + 7  -27

7. Vocabulary
Open Sentence – a mathematical statement (sentence) that contains one or more variables, or unknown numbers
An open sentence is neither true nor false until the variable(s) have been replaced by intended values from a given replacement set.
Replacement Set – intended values or a set of numbers that are substituted into an equation to determine if they are solutions or if they satisfy the open sentence

8. Vocabulary
Solving the open sentence means finding a value from the replacement set that will make the open sentence a true statement.
A solution means an element from the replacement set that makes the equation a true statement when substituted for the variable.
An open sentence may have one solution, more than one solution, or no solutions.

9. Vocabulary
Set means a collection of objects or numbers and are represented by using braces {}.
Element means one object or number or member of the set.
Sets are named by using capital letters. Examples of sets are A = {1,2,3,}; B = {6,8,10}; C= {1,2,3,6,8,10}.
The Solution set of an open sentence is the set of all elements from the replacement set that will satisfy or make the equation true when substituted for the variable.

10. Example: Equation Equations are separated by an equal sign
Numeric Expression
Variable Expression

11. Open Sentence Example 1 15 + x = 18, x = 3 15 + x = 18, x = 7
State whether the equation is true or false for the given value of the variable.
15 + x = 18, x = 3
15 + x = 18, x = 7

12. Open Sentence Example 2 5x = 15, x = 3 13 ÷ x = 5, x = 5 5(3) = 15
State whether the equation is true or false for the given value of the variable.
5x = 15, x = 3
5(3) = 15
13 ÷ x = 5, x = 5
13 ≠ 5 5

13. Open Sentence Example 3
Find the solution or solutions for the equation for a given SET of replacement values.

14. Open Sentence Example 4
Find the solution or solutions for the equation for a given SET of replacement values.

15. Open Sentence Example 5
Find the solution or solutions for the equation for the given replacement set.

16. Vocabulary: Inequality
<, , > or  are called inequality symbols.
x < y means “x is less than y”.
x  y means “x is less than or equal to y”.
x  y means “x is greater than y”.
x  y means “x is greater than or equal to y”.

17. Open Sentence Example 6
Find the solution or solutions for the equation for the given replacement set.

18. Open Sentence Example 7
Find the solution or solutions for the equation for the given replacement set.

19. Expression, equation, or inequality? 13x + 14y = 30
CHECKS FOR UNDERSTANDING
Expression, equation, or inequality? 13x + 14y = 30
Expression
Equation
Inequality

20. Expression, equation, or inequality? -2x - 4

21. Expression, equation, or inequality? 4b  21

22. Expression, equation, or inequality? 10a - 22 = -92

23. Expression, equation, or inequality? -7k  -35

24. The pay (P) at a certain job is calculated by multiplying the base pay (b) by the number of hours worked (h). If an employee works overtime (more than 40 hours in 1 week), the formula is P = 40b + 1.5b(h - 40). If Jamaal had base pay of $12.50/hr. and worked 46 hours, what would be his pay for the week?
$525.00
$575.00
$597.00
$612.50

25. If a side of the square shown has length 20, what is the area of the circle (A=πr2)?
1,257
125.6
68.8

26. Given 8 - x < 7, find the solution set if the replacement set is {0, 2, 4, 6, 8}.
Replace the variable (x) with each element in the replacement set and solve.
8 - 0 < < 7 False
8 - 2 < < 7 True
8 - 4 < < 7 True
8 - 6 < < 7 True
8 - 8 < < 7 True
The solution set is {2, 4, 6, 8}.

27. Given 5 = 10 - y, find the solution set if the replacement set is {1, 2, 3, 4}.
{1}
{1,2}
{1,2,3}
{1,2,3,4}
Null Set

28. Given 5 = 10 - y, find the solution set if the replacement set is {1, 2, 3, 4}.
5 = = 9 False
5 = = 8 False
5 = = 7 False
5 = = 6 False
None of these are true so the solution set is null set. Null set is a set with no elements.

29. What is the area of the shaded region?
10.37
10.75
42.52
127.5
Time permitting view homework
Read Section 1-3
do problems 18 – 26 on page 14