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Do Now:
Solve the following equations.
1.
2. 10 +
7x + 2 = 5x + 8
3.
y + 3 = 4y +13
4(2x - 5) = 5x + 4
4. A painting company charges $250 base plus $16 per
hour. Another painting company charges $210 base
plus $18 per hour. How long is a job for which the two
companies costs are the same?
Objective:
Students will be able to solve
equations to determine the number of
solutions.
Lesson 6.2
Equations with Variables on Both Sides
Identities and Contradictions
WORDS
NUMBERS
ALGEBRA
Identity
When solving an equation, if you get an
equation that is always true, the original
equation is an identity, and it has
infinitely many solutions.
2+1=2+1
3=3
2+x=2+x
–x
–x
2=2
Lesson 6.2
Equations with Variables on Both Sides
Identities and Contradictions
WORDS
NUMBERS
ALGEBRA
Contradiction
When solving an equation, if you get a
false equation, the original equation is a
contradiction, and it has no solutions.
1=1+2
1=3
x= x+3
–x –x
0=3
Lesson 6.2
Equations with Variables on Both Sides
Let’s Review…..
Steps on solving Multi-Step Equations
Don’t call me after midnight
1. D= Distributive property
2. C= combine like term
3. M = move variable to one side
4. A = addition/subtraction
5. M = Multiplication/division
Lesson 6.2
Equations with Variables on Both Sides
Example 1: Solve the following equations. Then
check your solution.
a.)
10 - 5x +1 = 7x +11-12x
Lesson 6.2
Equations with Variables on Both Sides
Example 1: Solve the following equations. Then
check your solution.
b.)
12x - 3+ x = 5x - 4 + 8x
Lesson 6.2
Equations with Variables on Both Sides
Example 1: Solve the following equations. Then
check your solution.
c.)
4y + 7 – y = 10 + 3y
d.)
2c + 7 + c = –14 + 3c + 21
Lesson 6.2
Equations with Variables on Both Sides
Example 2: Determine whether the following
have one solution, No Solution or infinitely many.
If it has one solution, find it.
a.) 12q –15
= 3(4q +3)
Lesson 6.2
Equations with Variables on Both Sides
Example 2: Determine whether the following
have one solution, No Solution or infinitely many.
If it has one solution, find it.
b.)
4(3x +1) – 7x = 6 + 5x – 2
Lesson 6.2
Equations with Variables on Both Sides
Example 2: Determine whether the following
have one solution, No Solution or infinitely many.
If it has one solution, find it.
c.)
4(-2x + 5) = -32x - 28
d.)
8x + 4(4x + 3) = 4 ( 6x + 4 ) - 4
Lesson 6.2
Equations with Variables on Both Sides
Guided Practice: Determine whether the
following have one solution, No Solution or
infinitely many. If it has one solution, find it.
1.) 2(3x + 2) = 6x + 4
2.) 8x – 3 = 15 + 5x
3.) 4x + 16 = 2x
4.) −7x − x + 2 = −8x − 8