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Happy Tuesday 
Ready for a great 4 day week
Warm – up #3
1. You have 128 ounces of milk and
drink 16 ounces per day. Write an
algebraic expression modeling the
amount of milk you have
2. Evaluate −𝑎2 − 2𝑎 − 7𝑏 + 𝑏
for a = - 2 and b = 3
Warm – up #3 Solutions
1.
128 – 16x
x = # of days
2. −𝑎2 − 2𝑎 − 7𝑏 + 𝑏
= −(−2)2 − 2 −2 − 7 3
= −4 − 2(−2) − 7(3) + 3
= −4 − −4 − 21 + 3
= −4 − −25 + 3
= −4 + 25 + 3
= 21 + 3 = 24
+ (3)
Lesson 1 – 4 Solving
Equations
Algebra II
Learning Objective
To solve equations
To solve problems by
writing equations
Properties of Equality
Reflexive Property
a = a
5 = 5
Symmetric Property
If a = b, then b = a
1
1
If = 0.5, then 0.5 =
2
Transitive Property
2
If a = b, and b = c, then a = c
If x = 3, and 3 = y, then x = y
Properties of Equality
Substitution
If a = b, then you can replace a
with b, and vice versa
If x = y and 9 + x = 15,
9 + y = 15
then
Properties of Equality
Addition Property
If a = b, then a + c = b + c
If x = 12, then x + 3 = 12 + 3
Subtraction Property
If a = b, then a – c = b – c
If x = 12, then x – 3 = 12 – 3
Properties of Equality
Multiplication Property
If a = b, then a ∙ c = b ∙ c
If x = 12, then x ∙ 3 = 12 ∙ 3
Division Property
If a = b, then a ÷ c = b ÷ c
If x = 12, then x ÷ 3 = 12 ÷ 3
(c ≠ 0)
Equation – a statement that two
expressions are equal
Solution(s) of the equation – All values
of the variable that make the
equation true
Inverse operations – operations that
“undo” each other. + & -
Solve a One-Step Equation
1. x + 4 = –12
–4=–4
x = –16
2. 12x = 18
12 12
3
x=
2
Solve a Multi-Step Equation
3. -27 + 6y = 3(y – 3)
-27 + 6y = 3y – 9
- 3y - 3y
-27 + 3y = –9
+27 + 27
3y = 18
3 3
y=6
Solve a Multi-Step Equation
4. 3(2x – 1) – 2(3x + 4) = 11x
6x – 3 – 6x – 8 = 11x
- 11 = 11x
11 11
x=-1
Solve a Multi-Step Equation
5. 11 + 3x – 7 = 6x + 5 – 3x
4 + 3x = 3x + 5
- 3x -3x
4=5
NEVER TRUE!!!
No Solution!!
Solve a Multi-Step Equation
6. 6x + 5 – 2x = 4 + 4x + 1
4x + 5 = 4x + 5
-5
-5
4x = 4x
-4x - 4x
0=0
ALWAYS TRUE!!!
Infinite Solution!!
Solve a Multi-Step Equation
7. 7x + 6 – 4x = 12 + 3x - 8
3x + 6 = 3x + 4
-3x
-3x
6=4
NEVER TRUE!!!
No Solution!!
Solve a Multi-Step Equation
8. 2x + 3(x – 4) = 2(2x – 6) + x
2x + 3x – 12 = 4x – 12 + x
5x – 12 = 5x – 12
+ 12
+ 12
5x = 5x
-5x - 5x
0=0
ALWAYS TRUE!!!
Infinite Solution!!
Literal Equation – an equation
that uses at least two different
letters as variables.
Can solve for any one of its
variables.
You solve for a variable “in
terms of” the other variables
Solve
a
Literal
Equation
5
9. C = 𝐹 − 32
9
What is F in terms of C?
9
5
C=[ 𝐹 −
5
9
9
C = F − 32
5
32 ]
9
5
+32
+ 32
9
C + 32 = F
5
9
𝐹 = C + 32
5
Solve a Literal Equation
Solve for x.
10.
2
𝑥+3
= 2𝑦 − 𝑤
2
𝑥+3
= 2𝑦 − 𝑤
2
x + 3 = 4y – 2w
-3
-3
x = 4y – 2w - 3
2
Solve a Literal Equation
Solve for x.
𝑎−𝑐
11.
=𝑚
2𝑥 − 𝑎
2x − a
𝑎−𝑐
2𝑥 − 𝑎
= 𝑚(2x – a)
a – c = 2mx - am
+ am
+ am
a – c + am = 2mx
2m
2m
𝑥=
𝑎 − 𝑐 + 𝑎𝑚
2𝑚
Using an equation to solve a
problem
12. A rectangle has a
perimeter of 200 meters. The
length is three times the width.
What are the dimensions of
the rectangle?
Width
Length
3x
x
Width = 25 m
Length = 75 m
P = 2(length) + 2(width)
200 = 2(3x) + 2(x)
200 = 6x + 2x
200 = 8x
8
8
x = 25
Assignment:
Pg. 30 #11-25 odd,
33-40 ALL