Transcript Ch 7.2 Solving Equations with Grouping Symbols

MJA
Ch 7.2 – Solving Equations with
Grouping Symbols
Bellwork

1.
2.
3.
Write the equation & solve
5x + 12 = 2x
1.7 + a = 2.5a – 4.9
7x + 3 = 2x + 23
Solution
-4
4
4.4
Assignment Review

Text p. 332 # 10 - 27
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…

Objective 7.2
Student will solve equations that have
grouping symbols
 Students will solve equations with no
solutions or an infinite number of
solutions

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
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!

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
Simplest Form

An algebraic equation is in its simplest
form when there are no like terms and no
grouping symbols
Example
5(a – 4) = 3(a + 1.5)
5a – 20 = 3a + 4.5
+ 20 =
Write the equation
Distributive Property
Add 20 to both sides
+ 20
5a
= 3a + 24.5
Simplify
-3a
= -3a
Subtract 3a from both sides
2a
=
24.5
2
=
2
a
=
12.25
Divide by 2
Solution
Your Turn

1.
2.
In the notes section of your notebook
write and solve the equations
3h = 5(h – 2)
6(b – 2) = 3(b + 8.5)
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…
Example
3x + 2 = 3x - 1
Write the equation
-3x
Subtract 3x from both sides
= -3x
+2=
-1
+2≠
-1
Solution: ø
Result is not a true statement
The solution is a null set
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….
Example
2(2x – 1) + 6 = 4x + 4
4x – 2 + 6 = 4x + 4
4x + 4 = 4x + 4
-4=
4x
4
x
-4
Write the equation
Distributive Property
Simplify
Subtract 4 from both sides
= 4x
= 4
= x
Divide both sides by 4
The equation x = x is always true.
The solution set is the set of all numbers
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

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
