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SOL 7.12: Equations Prep

I can solve two-step linear equations in one variable, including practical problems that require the solution of a two-step linear equation in one variable.

Two-Step Equations Tips

• Isolate the variable

• What you do to one side you must do to the other

• Use inverse (opposite) operations to solve

• "Undo" addition/subtraction first, then multiplication/division

• equations can be modeled using colored chips, algebra tiles, or weights on a balance scale

• An equation is a mathematical sentence that states that tow expressions are equal

• Always check your answers!

Multiple Choice

 $2x+5=23$  
Solve for x.

• -9

• -14

• 9

• 14

Tips for verbal sentences....

• watch for turn around words: less than, subtracted from

• "is" means =

Multiple Choice

Which equations means "a number increased by the product of 7 and 12 is 93"?

• $7x+12=93$

• $7x+12x=93$

• $\left(x+7\right)\left(12\right)=93$

• $x+\left(7\right)\left(12\right)=93$

Multiple Choice

• 5

• -2

• 2

• -5

Multiple Choice

Ms. Alvey's scarf is 4 inches more than half the length of Mrs. Watson's scarf. Ms. Alvey's scarf is 34 inches long. How long is Mrs. Watson's scarf?

• 15 inches

• 60 inches

• 112 inches

• 128 inches

Multiple Choice

What is the equation shown in this picture?

• $3x=7$

• $-3x=-7$

• $x-3=-7$

• $x+3=7$

Multiple Choice

Solve for x.

• $x=-4$

• $x=\frac{7}{3}$

• $x=4$

• $x=-10$

Multiple Choice

Which of the algebraic equations below represents the following verbal sentence?

Seven less than a number is eight

• $7-x=8$

• $x-7=8$

• $-7x=8$

• $7+x=8$

Multiple Choice

Which of the algebraic equations below represents the following verbal sentence?

A number decreased by nine is twelve

• $9-n=12$

• $n-9=12$

• $9n=12$

• $12-9=n$

Multiple Choice

• 8

• 16

• 4

• 10

Multiple Choice

 $6x-4=32$  

Which verbal sentence represents the equation above?

• the product of six and a number less than 4 is 32

• the quotient of six and a number, minus four is 32
  

• six times the difference of x and 4 is 32

• Four less than the product of six and a number is 32

Literal Equations

Equations with multiple variables

Multiple Choice

A-B = C

(solve for A)

• A = C - B

• A = C + B

• A - C = B

• B = A - C

Solve for r

• rt means r times t (multiplication)

• Opposite (inverse operation) is division

• Divide both sides by t

Multiple Choice

 $g\ =\ 6x\ \ \ solve\ for\ x$  

•  $x\ =\ \frac{g}{6\ }$  

•  $x\ =\ \frac{6}{g}$  

•  $x\ =\ g+6$  

•  $x\ =\ g-6$  

Open Ended

How do you think I could get y by itself?

Getting y by itself

• kx go together so they are one term

• kx is being added

• The opposite of addition is subtraction

• Subtract kx from both sides

Open Ended

What is the first step to get x by itself?

Multiple Choice

How can we get x by itself?

• Add k

• Subtract k

• Multiply by k

• Divide by k

Multiple Choice

2h = w-3p

(solve for p)

• p = (2h - w) / -3

• p = (2h - w) / 3

• p = -6hw

• p = -6h - 3w

Multiple Choice

Solve for v

C = xv + x

• (C-x)/x = v

• (C+x)/x = v

• (-C-x)/x = v

• (Cx)/x = v

Multiple Choice

ax + c = R
(solve for x) 

• ax = R + c
• ax = R - c
• x = a(R-c)
• x = (R-c) / a 

Equations with Parentheses - Solve for h

Multiple Choice

What is the next step t get h by itself?

• Add R

• Subtract R

• Multiply by R

• Divide by R

Multiple Choice

Solve for n

• A

• B

• C

• D

2.6 Ratios, Rates, and Conversions

Quick Overview

2.7 ​Solving Proportions

Objective:

• ​Students will be able to solve and apply proportions.

2-8 Proportions and Similar Figures

Guided Notes

Multiple Choice

A model of a house was built using the scale 5 in:25 ft. If a window in the model is 1.5 in. wide, how wide is the actual window?

• 90 ft
• 7.5 ft 
• 4.5 ft
• 45 in

Multiple Choice

On a certain map, 1 inch represents 20 miles. If two towns are 3.25 inches apart on the map, how far apart are they in real life?

• 65 miles

• 6 miles

• 20 miles

• 100 miles

Multiple Choice

Solve for X.

• 2 ft
• 3 ft
• 4 ft
• 6 ft

Multiple Choice

The pair of figures is similar. Find the missing side.

• x = 10
• x = 4
• x = 2
• x = 5

Monday 2.1 Decimals, Percents & Fractions

​

Percents to Fractions

Multiple Choice

20% is what fraction?

• 1/5
• 2/5
• 1/2
• 1/4

Multiple Choice

What is 4% as a fraction (in lowest terms)?

• 40/100
• 1/25
• 4/10

Percent to decimal

Multiple Choice

What is 7% as a decimal?

• 7.0
• .7
• .07

Multiple Choice

What is 225% as a decimal?

• 2.25
• .225
• 255.5

Decimals to Percents

Multiple Choice

Write 0.002 as a percent 

• 0.02%
• 2%
• 0.2%
• .2

Multiple Choice

Write 0.555 as a percent 

• 55.5%
• 555%
• 55%
• 5.555%

Multiple Choice

Write 1.5 as a percent 

• 015%
• 1.5%
• 15%
• 150%

Multiple Choice

Write 0.8 as a percent

• 8%
• 80%
• 0.08
• 88%

Fractions to decimals

Multiple Choice

Write  $2\ \frac{5}{10}$  as a decimal. 

• 2.05

• 2.5

• 25.1

• 2.510

Multiple Choice

Write 52/100 as a decimal

• 5.2

• .052

• 52.100

• .52

Multiple Choice

Write 4/10 as a decimal

• .04

• .4

• 4.0

• .410

Fractions to Percents

Multiple Choice

Write 11/25 as a percent

• 11%
• 44%
• 22%
• 55%

Multiple Choice

What is 3/100 as a percentage?

• 300%
• 30%
• 3000%
• 3%

Multiple Choice

What is 12/100 as a percentage?

• 24 %
• 12 %
• 50 %
• 99 %

C2L2 Proportions with Percents

Mrs. Spencer

​Algebra 1A

​C2L2 Vocabulary Notes

• ​Design: The strategy used for the collection, measurement, and analysis of data

• ​Sample: a set of items from a larger collection

• ​Simulate: To model an experiment with another experiment

• ​A percent proportion is an equation where a percent is equal to an equivalent ratio.

Multiple Choice

Complete the definition:

A _________ consists of all subjects (human or otherwise) that are being studied

• Statistics

• Number

• People

• Population

• Pueblo

Multiple Choice

Complete the definition:

A _______ is a subset of a population

• sample

• people

• population

• group

Multiple Choice

Write a proportion and solve:
Eight is what percent of 64?

• 12.5%
• 8%
• 800%
• 1/8

Multiple Choice

Write a proportion and solve:
Six is what percent of 5?

• 120%
• 83.3%
• 132%
• 64%

Multiple Choice

Write a proportion and solve:
Thirty is 20% of what number?

• 150
• 6
• 143
• 18

​Review

Percent

• Percent is the amount per hundred

• ​Percent is a number used to show the relationship of part to whole

• ​The ratio of the part to the whole can be written as an equivalent ratio with 100 in the denominator

• ​Part (is), Whole (of), Percent (%)

Set up a proportion and solve for the unknown

Multiple Choice

Allison used a 30% off coupon to purchase a sweater. If she saved $14.40, what was the original price of the sweater?

• $45.20

• $48.00

• $52.40

• $54.00

Multiple Choice

Yulia went to the clearance rack at a department store and found a shirt she wanted to buy.  The shirt was $36.00 and is on sale for $24.00.  What is the percent of the decrease?

• 33%
• 67%
• 50%
• 34%

Multiple Choice

Tickets to Disneyland are $100. The price is going to increase on January 1. What is the percent of change if the cost increases to a $120?

• 25%
• 120%

• 20%
• 50%

Multiple Choice

Juan has a coupon for 25% off her entire meal of $17.89.

What is the discount (amount he will save)?

• $13.42
• $4.47
• $4.48
• $0.44

Multiple Choice

78 is what percent of 450?

• 5%
• .17
• 17%
• 18%

More Examples​ - Take notes

​Example A - Finding an Unknown Percent

​In a capture-recapture process, 200 fish were tagged. From the recapture result, the game warden estimates that the lake contains 2500 fish.

​

What percent of the fish were tagged?

​

​Step 1: Set up a proportion

​

​Step 2: Solve for the unknown

​

​Step 3: Write the solution to the problem in words

​Example B - Finding an Unknown Total

​​In a lake with 250 tagged fish, recapture results show that 11% of the fish are tagged.

​

​About how many fish are in the lake?

​

​Step 1: Set up a proportion

​

​Step 2: Solve for the unknown

​

​Step 3: Write the solution to the problem in words

​Example C - Finding an Unknown Part

A lake is estimated to have 5000 fish after recapture experiments that showed 3% of the fish were tagged.

​

​How many fish were originally tagged?

​

​Step 1: Set up a proportion

​

​Step 2: Solve for the unknown

​

​Step 3: Write the solution to the problem in words

Multiple Choice

34% of what number is 51?

• 69
• 71
• 150
• 196

Multiple Choice

A student made an 85% on a test with 25 questions. What is the number of questions that the student answered correctly?

Round to the nearest whole number.

• 21 questions

• 22 qestions

• 23 questions

• 24 questions

Multiple Choice

There are 36 quarters in my coin collection. If my coin collection has 45% quarters, how many total coins do I have?

• 75%

• 80 %

• 75 coins

• 80 coins

Multiple Choice

Jose and his family are enjoying a vacation in Arizona. One place they really want to visit is the Grand Canyon. The total distance they will drive is 400 miles. If they have already driven 280 miles, what percent have they driven?

• 68%

• 30%

• 70%

• 43%

Multiple Choice

Leslie's class has 28 students in it. 25% of those students are home sick today. How many students are home sick?

• 4 students

• 7 students

• 11 students

• 13 students

Multiple Choice

The 9th graders at CCECHS are going to the Dodger game. 60% of the 120 students want to go to downtown LA first. How many students want to go downtown LA first?

• 72 students

• 27 students

• 54 students

• 69 students

Poll

Rate your understanding of this lesson (1 -Low to 5-High),

Action Items:  Watch more videos, redo the lesson, do more practice problems, review the notes, ask questions, take more notes, write down more examples, etc.

• 1- I need help! Pick 3 items.

• 2- I think I have it. Pick 2-3 items.

• 3-Need practice. Pick 1-2 items.

• 4-Pretty Good. Pick 1 item.

• 5-Got it. Help a classmate get it too.