1. Ch 7.2 – Solving Equations with Grouping Symbols
MJA
Ch 7.2 – Solving Equations with Grouping Symbols

2. Bellwork Write the equation & solve 5x + 12 = 2x 1.7 + a = 2.5a – 4.9
Solution
- 4 4
4.4

3. Assignment Review
Text p. 332 #

4. Before we begin… Please take out your notebook and get ready to work…
Yesterday we worked with solving equations with variables on both sides of the equation…
In today’s lesson we will look at how to solve equations using grouping symbols…

5. Objective 7.2 Student will solve equations that have grouping symbols
Students will solve equations with no solutions or an infinite number of solutions

6. Quick Review Grouping Symbols
Parenthesis ( ) are grouping symbols
Brackets { } are grouping symbols
Fraction Bars are grouping symbols
According to the order of operations when solving equations work with the grouping symbols first
If you have multiple grouping symbols work with the inside grouping symbols first…That is if you have parenthesis nested within brackets you do the parenthesis first

7. Quick Review
Distributive Property – earlier this year we discussed the distributive property which may look like this: 3(x + 5)
Generally, what this is saying is to multiply the 3 by everything within the brackets.
When you see a number like 3 next to a bracket with no operation sign, then it means to multiply
You are required to be able to recognize and know how to work with the distributive property!

8. Distributive Property Review
3 (x + 5) 3x
+ 15
Make sure that you multiply what on the outside of the parenthesis with EVERYTHING on the inside of the parenthesis

9. Simplest Form
An algebraic equation is in its simplest form when there are no like terms and no grouping symbols

10. Example 5(a – 4) = 3(a + 1.5) 5a – 20 = 3a + 4.5 + 20 = + 20
Write the equation
5a – 20 = 3a + 4.5
Distributive Property
+ 20 =
Add 20 to both sides
5a = 3a
Simplify
-3a = -3a
Subtract 3a from both sides
2a =
Divide by 2 =
a =
Solution

11. Your Turn
In the notes section of your notebook write and solve the equations
3h = 5(h – 2)
6(b – 2) = 3(b + 8.5)

12. No Solution
Some equations have no solutions. That is no value of the variable will result in a true statement.
The solution set is called the null or empty set and is designated with the following symbols: ø or { }
Let’s look at an example…

13. Example 3x + 2 = 3x - 1 -3x = -3x + 2 = - 1 + 2 ≠ - 1 Solution: ø
Write the equation
-3x = -3x
Subtract 3x from both sides
+ 2 =
Result is not a true statement
+ 2 ≠
Solution: ø
The solution is a null set

14. Infinite Solutions
Some equations have all numbers as their solution set.
An equation that is true for every value of the variable is called an identity
Let’s look at an example….

15. Example 2(2x – 1) + 6 = 4x + 4 4x – 2 + 6 = 4x + 4 4x + 4 = 4x + 4
Write the equation
4x – = 4x + 4
Distributive Property
4x + 4 = 4x + 4
Simplify
- 4 =
Subtract 4 from both sides
4x = 4x
Divide both sides by 4
= 4
x = x
The equation x = x is always true.
The solution set is the set of all numbers

16. Summary
In the notes section of your notebook summarize the key concepts covered in today’s lesson
Today we discussed:
Solving equations with grouping symbols
Null & empty sets
Identity

17. Assignment Text p. 337 # 20 – 33 Reminder:
This assignment is due tomorrow
I do not accept late assignments
You must show your step by step solution to each of the problems