The document provides examples for solving linear equations using the work backward strategy. It includes 4 example equations with the step-by-step work shown. The answers are then provided. Additional material is included on equivalence, solving equations with variables on both sides, and using properties of equality.
Read| The latest issue of The Challenger is here! We are thrilled to announce that our school paper has qualified for the NATIONAL SCHOOLS PRESS CONFERENCE (NSPC) 2024. Thank you for your unwavering support and trust. Dive into the stories that made us stand out!
The simplified electron and muon model, Oscillating Spacetime: The Foundation...RitikBhardwaj56
Discover the Simplified Electron and Muon Model: A New Wave-Based Approach to Understanding Particles delves into a groundbreaking theory that presents electrons and muons as rotating soliton waves within oscillating spacetime. Geared towards students, researchers, and science buffs, this book breaks down complex ideas into simple explanations. It covers topics such as electron waves, temporal dynamics, and the implications of this model on particle physics. With clear illustrations and easy-to-follow explanations, readers will gain a new outlook on the universe's fundamental nature.
MATATAG CURRICULUM: ASSESSING THE READINESS OF ELEM. PUBLIC SCHOOL TEACHERS I...NelTorrente
In this research, it concludes that while the readiness of teachers in Caloocan City to implement the MATATAG Curriculum is generally positive, targeted efforts in professional development, resource distribution, support networks, and comprehensive preparation can address the existing gaps and ensure successful curriculum implementation.
This slide is special for master students (MIBS & MIFB) in UUM. Also useful for readers who are interested in the topic of contemporary Islamic banking.
it describes the bony anatomy including the femoral head , acetabulum, labrum . also discusses the capsule , ligaments . muscle that act on the hip joint and the range of motion are outlined. factors affecting hip joint stability and weight transmission through the joint are summarized.
How to Add Chatter in the odoo 17 ERP ModuleCeline George
In Odoo, the chatter is like a chat tool that helps you work together on records. You can leave notes and track things, making it easier to talk with your team and partners. Inside chatter, all communication history, activity, and changes will be displayed.
This presentation includes basic of PCOS their pathology and treatment and also Ayurveda correlation of PCOS and Ayurvedic line of treatment mentioned in classics.
Safalta Digital marketing institute in Noida, provide complete applications that encompass a huge range of virtual advertising and marketing additives, which includes search engine optimization, virtual communication advertising, pay-per-click on marketing, content material advertising, internet analytics, and greater. These university courses are designed for students who possess a comprehensive understanding of virtual marketing strategies and attributes.Safalta Digital Marketing Institute in Noida is a first choice for young individuals or students who are looking to start their careers in the field of digital advertising. The institute gives specialized courses designed and certification.
for beginners, providing thorough training in areas such as SEO, digital communication marketing, and PPC training in Noida. After finishing the program, students receive the certifications recognised by top different universitie, setting a strong foundation for a successful career in digital marketing.
Executive Directors Chat Leveraging AI for Diversity, Equity, and InclusionTechSoup
Let’s explore the intersection of technology and equity in the final session of our DEI series. Discover how AI tools, like ChatGPT, can be used to support and enhance your nonprofit's DEI initiatives. Participants will gain insights into practical AI applications and get tips for leveraging technology to advance their DEI goals.
Thinking of getting a dog? Be aware that breeds like Pit Bulls, Rottweilers, and German Shepherds can be loyal and dangerous. Proper training and socialization are crucial to preventing aggressive behaviors. Ensure safety by understanding their needs and always supervising interactions. Stay safe, and enjoy your furry friends!
Introduction to AI for Nonprofits with Tapp NetworkTechSoup
Dive into the world of AI! Experts Jon Hill and Tareq Monaur will guide you through AI's role in enhancing nonprofit websites and basic marketing strategies, making it easy to understand and apply.
Introduction to AI for Nonprofits with Tapp Network
(8) Lesson 2.4 - Solve Equations with Variables on Each Side
1. Course 3, Lesson 2-4
Use the work backward strategy to solve Exercises 1-3.
1. Alicia arrived home at 7:45 P.M. from a restaurant. She spent 45
minutes waiting in the restaurant lobby and one and a half hours eating
dinner. If it took her 20 minutes to drive home, what time did she arrive
at the restaurant?
2. Marcus has $6 left over after his trip to the movie theater. If his movie
ticket cost $5.50 and he purchased a drink for $3.00, and a bag of
popcorn for $3.50, and a box of candy for $2.00, how much money did
he originally take to the movie theater?
3. Candace’s quiz scores are 86, 98, 85, 94, and 89. What is the minimum
score she can make on her next quiz to maintain a quiz average of at
least 90?
4. At nine months of age, a baby elephant can weigh 700 pounds. If this is
4 times the baby elephant’s birth weight, how many pounds did the
elephant weigh at birth?
6. To solve equations with
• variables on both sides
• rational coefficients
Course 3, Lesson 2-4
Expressions and Equations
7. 1
Need Another Example?
2
3
4
Step-by-Step Example
1. Solve 8 + 4d = 5d. Check your solution.
8 + 4d = 5d Write the equation.
Write the original equation.Check 8 + 4d = 5d
8 = d
Subtraction Property of Equality
To check your solution, replace d with 8 in the original equation.
Simplify by combining like terms.
Subtract 4d from the left side of
the equation to isolate the variable.
Subtract 4d from the right side of
the equation to keep it balanced.
Replace d with 8.
The sentence is true.
8 + 4(8) = 5(8)
40 = 40
?
–4d = – 4d
11. 1
Need Another Example?
2
3
4
5
6
Step-by-Step Example
3. Green’s Gym charges a one time fee of $50 plus $30 per session for a personal
trainer. A new fitness center charges a yearly fee of $250 plus $10 for each session
with a trainer. For how many sessions is the cost of the two plans the same?
20s = 200
Simplify.
Check Green’s Gym: $50 plus 10 sessions at $30 per session
Simplify.
Addition Property of Equality
50 + 10 • 30 = 50 + 300
250 + 10 • 10 = 250 + 100
50 + 20s = 250
Subtraction Property of Equality
Write the equation.50 + 30s = 250 + 10s
fee of $50 plus
$30 per session
Words
Let s represent the number of sessions.Variable
50 + 30s = 250 + 10sEquation
is the
same as
a fee of $250 plus
$10 per session
Division Property of Equality
s = 10
So, the cost is the same for 10 personal trainer sessions.
Simplify.
= $350
new fitness center: $250 plus 10 sessions at $10 per session
= $350
– 10s = – 10s
– 50 = – 50
12. Answer
Need Another Example?
The measure of an angle is 8 degrees more than its
complement. If x represents the measure of the angle and
90 – x represents the measure of its complement, what is
the measure of the angle?
49°
13. 1
Need Another Example?
2
3
4
Step-by-Step Example
4. Solve x – 1 = 9 – x.
x = 12
Simplify.
Multiplicative Inverse Property
Addition Property of Equality
The common denominator of the coefficients is 6.
Rewrite the equation.
Addition Property of Equality
Simplify.
Simplify.
+ 1 = + 1
15. How did what you learned
today help you answer the
WHAT is equivalence?
Course 3, Lesson 2-4
Expressions and Equations
16. How did what you learned
today help you answer the
WHAT is equivalence?
Course 3, Lesson 2-4
Expressions and Equations
Sample answers:
• When variables are on both sides of the equation, use
the properties of equality to write an equivalent
equation with the variables on one side.
• You can check the solution to an equation by replacing
the variable with the solution in the original equation.
17. Name the procedures you
would use to solve an
equation with variable terms
on both sides such as
3x + 5 = 6x + 2.
Course 3, Lesson 2-4
Ratios and Proportional RelationshipsExpressions and Equations