Download 2.3 honors powerpoint

Objective: To solve one-step, two-step and multi-step
equations involving clearing fractions and decimals.
Do now: Copy the scale and answer the
question below.
What is the weight of a blue bar in terms
of green squares?
Introduction to Equations HW
1. In your own words, what is an
equation?
2. Describe the ways in which an
equation is like a balance scale.
3. When solving an equation, why must
you perform the same operations on
each side of the equation?
4. How is an algebraic equation like
5𝑥 + 3 = 8 different from an algebraic
expression like 5𝑥 + 3?
Pre-assessment final answers:
1. 𝑥 – 12 – 3𝑥 − 2𝑥 = 38
x=25
2. 0.2𝑦 + 2.9 – 0.8𝑦 = 0.5
y=4
𝟏𝟎 0.2𝑦 + 2.9 – 0.8𝑦 = 0.5
2𝑦 + 29 − 8𝑦 = 5
2
−
8
𝑥
+
6
2
𝟐𝟒(−
8
𝑥
+
6
3.
𝐿𝐶𝐷
+
7
8
+
7
8
=
7
8
=
7
8
𝟑
x=
𝟐
)
−6 + 4𝑥 + 21 = 21
An equation is a mathematical statement that two
quantities are the same.
A solution is a value that makes the statement true.
Check steps?
Based on your performance and
confidence level on your homework
assignment, choose a classwork task!
If you…
circled 1-2 OR
unfamiliar with
clearing fractions
and decimals
circled 3-4
circled 5 and am
confident about how
to clear fractions and
decimals
take…
2.3 Review
for Mastery
2.3 Practice
2.3 Challenge
To do…
1. Hand in Intro to Equations HW handout!
2. Pick up “How-To” & Classwork Assignment
If you…
circled 1-2 OR
unfamiliar with
clearing fractions
and decimals
circled 3-4
circled 5 and am
confident about how
to clear fractions and
decimals
take…
2.3 Review
for Mastery
& key
2.3 Practice
& key
2.3 Challenge
& key
• Work to complete your task.
• You may work with a partner.
• You will have an exit card at
the end of the period.
Clearing Fractions or Decimals Exit Card
Solve each equation. Show all work including check steps.
1.
3.
6 − 2 𝑥 − 5 = 66
𝑥
6
+
5
8
=
7
8
2.
𝑛
4.
0.05x + 24.65 = 27.5
3
+
𝑛
4
= 7
3. Reflect on today's lesson.
a. At the beginning of today's lesson, my confidence level with this material was at
1
2
b. At the end of today's lesson, my confidence level with this material is at
3
4
1
2
3
5.
c. In order to improve my level of confidence, I need to ______________________________
__________________________________________________________________________. OR
Since I am confident about this material, I can help my peers by ______________________
____________________________________________________________________________.
4
5.
HOMEWORK
Section 2-3
pg. 92-93, #9-10, 12, 35-53 odds
Objective: To solve multi-step equations.
Warm Up: Solve.
1. 4x+4-5x=10
2. 3-2(x+1)=-7
Check Homework!
Score # correct out of total
number.
Split up into two groups!
1. Meet with Ms. Hornick to
clarify HW questions and
material from last week.
2. Find the mistake!
2.3 Multi-Step Equations
Vocabulary:
An equation is a mathematical statement
that two expressions are equal.
A solution of an equation is a value of the
variable that makes the equation true.
To find solutions, isolate the variable. A
variable is isolated when it appears by itself
on one side of an equation, and not at all on
the other side.
Isolate a variable by using inverse operations
which "undo" operations on the variable.
An equation is like a balanced scale. To keep the
balance, perform the same operation on both
sides.
Inverse Operations
Operation
Addition
Subtraction
Inverse Operation
Subtraction
Addition
Solving an equation that contains multiplication or
division is similar to solving an equation that
contains addition or subtraction. Use inverse
operations to undo the operations on the variable.
Inverse Operations
Operation
Multiplication
Division
Inverse Operation
Division
Multiplication
Remember that dividing is the same as
multiplying by the reciprocal. When
solving equations, you will sometimes
find it easier to multiply by a reciprocal
instead of dividing. This is often true
when an equation contains fractions.
Example 1:
Solve the equation.
5
w = 20
6
The reciprocal of 5 is 6 . Since w is
6
5
5
multiplied by , multiply both sides
6
6
by
.
5
w = 24
Check
5
w = 20
6
20
20 20 
To check your solution,
substitute 24 for w in the
original equation.
Find the mistake!
They didn’t multiply
by the reciprocal!
-2(x-1)+1=5
This is called a multi-step equation.
Steps to Solve:
- Simplify the expression on each side.
- Use inverse operations in reverse
PEMDAS order.
(undo addition/subtraction)
(undo multiplication/division)
-Always check your answer!
Example 2:
Solve -2(x-1)+1=5
. -2x+2+1 = 5
-2x + 3 = 5
–3 – 3
-2x = 2
-2
-2
x= -1
Simplify each side.
Undo addition by 3. Subtract 3 from
both sides.
Undo multiplication by -2. Divide both
sides by -2.
Example 3:
Solve 10y – (4y + 8) = –20
Write subtraction as addition
10y + (–1)(4y + 8) = –20
of the opposite.
10y + (–1)(4y) + (–1)( 8) = –20 Distribute –1 on the left side.
10y – 4y – 8 = –20 Simplify.
6y – 8 = –20 Combine like terms.
+8
+ 8 Since 8 is subtracted from 6y,
add 8 to both sides to
6y = –12
undo the subtraction.
6y = –12 Since y is multiplied by 6,
divide both sides by 6 to
6
6
undo the multiplication.
y = –2
Example 4:
a. If 5t – 2 = –32, find the value of 3t+10
5t – 2 = –32
+2
+2
5t
= –30
5t = –30
5
5
t = –6
First t is multiplied by 5. Then 2 is
subtracted. Work backward: Add 2
to both sides.
Since t is multiplied by 5, divide both
sides by 5 to undo the multiplication.
3t+10 = 3(–6) + 10 = -18 +10 = -8
Example 5:
Solve 8x – 21 + 5x = –15.
8x – 21 – 5x = –15
8x – 5x – 21 = –15
3x – 21 = –15 Combine like terms.
+ 21 +21 Since 21 is subtracted from 3x, add 21
to both sides to undo the subtraction.
3x = 6
Since x is multiplied by 3, divide both
sides by 3 to undo the multiplication.
x=2
You Try: Example 6
Solve 4(x – 2) + 2x = 40
4(x – 2) + 2x = 40
(4)(x) + (4)(–2) + 2x = 40
4x – 8 + 2x = 40
4x + 2x – 8
6x – 8
+8
6x
= 40
= 40
+8
= 48
6x = 48
6
6
x=8
Distribute 4 on the left side.
Simplify.
Commutative Property of Addition.
Combine like terms.
Since 8 is subtracted from 6x, add
8 to both sides to undo the
subtraction.
Since x is multiplied by 6, divide
both sides by 6 to undo the
multiplication.
2.3 Practice B/C
Define your variables, write an equation, and solve. Write
your solution in a complete sentence.
6.
The two angles shown form a right angle. Write
and solve an equation to find the value of x.
7.
For her cellular phone service, Vera pays $32 a
month, plus $0.75 for each minute over the allowed minutes
in her plan. Vera received a bill for $47 last month. For how
many minutes did she use her phone beyond the allowed
minutes?
Work on Practice 2.3 B/C
Don’t forget to show check
steps for each problem!
Example 3 Continued
Solve
.
3y = 32
3
3
Since y is multiplied by 3, divide
both sides by 3 to undo the
multiplication.
You try: Example 4 - Clearing Fractions First!
Solve
.
Multiply by the LCD to clear the fractions.
Multiply both sides by 12, the LCD
of the fractions.
Distribute 12 on the left side.
8r + 9 = 7
–9 –9
8r = –2
Simplify. Since 9 is added to 8r,
subtract 9 from both sides to
undo the addition.
You Try: Example 4 Continued
Solve
.
8r = –2
8
8
Since r is multiplied by 8, divide
both sides by 8 to undo the
multiplication.
Example 3: Clearing Fractions First!
Solve
.
Multiply by the LCD to clear the fractions.
Multiply both sides by 24,
the LCD of the fractions.
Distribute 24 on the left side.
3y – 18 = 14
+18 +18
3y = 32
Simplify.
Since 18 is subtracted from 3y, add
18 to both sides to undo the
subtraction.
You Try: Example 5 Continued
Solve
4x = 55
4
4
.
Simplify. Since 4 is multiplied by x, divide
both sides by 4 to undo the
multiplication.
Equations that are more complicated may
have to be simplified before they can be
solved.
You may have to…
•use the Distributive Property and/or
•combine like terms
before you begin using inverse operations.
You Try: Example 5
Solve
.
Method 2 Multiply by the LCD to clear the fractions.
Multiply both sides by 10, the LCD
of the fractions.
Distribute 10 on the left side.
4x – 5 = 50
+5 +5
4x = 55
Simplify.
Since 5 is subtracted from 4x,
add 5 to both sides to undo the
subtraction.