Linear EquationsChapter 2

Writing Equations

Key words that indicate you have an equal sign

IsIs as much asIs the same asIs identical to

Translate sentences into Equations

Seven times a number squared is five times the difference of k and m

Fifteen times a number subtracted from 80 is 25.

The quotient of a number and 8 increased by 2 is 16.

The product of 27 and k is h squared decreased by 9

Assign a Variable to Model Word ProblemsThere are approximately 87,000

flights per day in the United States. How many days will it take for 261,000 to have occurred?

There are 50 members in the North Carolina Senate. This is 70 fewer than the number of North Carolina House of representatives. How many members are in the North Carolina House of Representatives?

Model geometric formulas

Area of a trianglePerimeter of a rectangleVolume of a sphereSurface area of a rectangular prism

The Pythagorean TheoremEtc….

Translate Equations into Sentences

6z – 15 =- 45y2 + 3x = 4(3/2)r – t3 = 13212 – 2x = (5 + x)/2

Write a Word Problem

Let t = the time that Maxine drove in each turn

t + 4= the time that Tia drove in each turn

2t + (t+4) = 28

Let m= Max’s salary

.1s = Max’s bonus m + .1m = 525

Let f = cost of fries f + 1.50 = cost of

a burger

4(f + 1.50) – f = 8.25

Solving One Step Equations

Whatever you do on one side, you MUST do on the other

INVERSE Operations undo each other

Dividing is the same as multiplying by the reciprocal

The operation to be “undone” is the operation being done on the VARIABLE!

Solving Multiple Step Equations

SimplifyWrite the equation with the least amount of variables, numbers, and operations

Undo Addition and SubtractionUndo Multiplication and Division

Solving Multiple Step Equations

11x – 4 = 29(a + 7)/8 = 512 = -7f – 9-3 = 2 + a/11(3/2)a – 8 = 11

Model and Solve

Chris is buying a pair of water skis that are on sale for 2/3 of the original price. After, he uses a $25 gift certificate, the total before tax is $115. What was the original price of the skis?

Len read ¾ of a graphic novel over the weekend. Monday he read 22 more pages. If he had read 220 pages, how many pages does the book have?

Solve

Find three consecutive integers with a sum of 21

Modeling with Some Number Theory

Consecutive Integers

Consecutive Even Integers

Consecutive Odd Integers

n, n+1, n+2, n + 3,…

n, n+2, n+4, ….

n, n + 2, n + 4, …

How can odd and even patterns be the same???

Model and Solve

Find three consecutive odd integers with a sum of -51

Solving Equations with Variables on both sides with lots of stuff!

2 + 5k = 3k – 6x/2 + 1 =( ¼)x – 61.3c = 3.3c + 2.86(5m – 3) = 1/3 (24m + 12)5x + 5 = 3(5x – 4) – 10x3(2b – 1) – 7 = 6b - 10

Absolute Value

The distance a number is from zero on a number line

Always a positive numberDenoted with n 6 -4- 8

Absolute Value Expressions

Evaluate: m + 6 – 14, Let m = 4

23 - 3 – 4x , Let x = 2

Absolute Value Equations

f + 5 = 17

b – 1 = -3

3n – 4 = 6

Extend Ratios and Proportions

Means and Extremes

a:b = c:d

a = c b d

Solving Proportions

x = 3 10 5

x-2 = 2 14 7

x + 4 = 3 5 8

Proportions and Problem Solving

It takes 7 minutes for Bella to walk around the gym track. At this rate, how many times can she walk around the track in half an hour?

The Ramsey Cascade Trail is about 1 1/8 inches long on a map with scale

3 inches = 10 miles What is the actual length of the trail?

Ratios and Unit ConversionsHow many miles long is a 10K race? (1 meter = 1.094 yards, 1 mile = 1760 yards)

How many square feet = 2000 sq inches?

How many gallons = 920 cups?

How many ft/sec is 25 mi/hour?

How many km/hr is 55 mi/hr?

Debt to Income Ratio

P. 119

Percent of Change

Change “over” original!!!

Ex.Original: 66 New: 30

Original: 24 New: 40

The total number of passengers on cruise ships increased 10% from 2007 -2009. If there were 17.22 million passengers in 2009, how many were there in 2007?

Solving for a Specific Variable

Use the formula for the area of a triangle to solve for the height.

Find the radius for the circumference of a circle.

Solve for m: 4m – 3n = 8Solve for q: a(q – 8) = 23Solve for x: 3x – 2y = xz + 5

Chart Problems

Two or more parts are combined into a whole

More than one relationship is contained in the problem

Ex. Weighted averages (marking period

grades, baseball slugging average) Mixture Problems Percent Mixture Problems Uniform Motion Problems

Mixture Problems

A tea company sells blended tea for $25 per pound. To make blackberry tea, dried blackberries that cost $10.50 a pound are blended with black tea that costs $35 per pound. How many pounds of black tea should be added to 5 pounds of dried blackberries to make blackberry tea?

Another Example

Premium coffee sells for $9.50/ pound, supreme sells for $11.75/pound, and a blend sells for $10.00/pound. How many pounds of Premium coffee beans should be mixed with 2 pounds of Supreme coffee to make the coffee blend?

Percent Mixture Problem

Mrs. Matthews has 16 cups of punch that is 3% pineapple juice. She also has a punch that is 33% pineapple juice. How many cups of the 33% punch will she need to add to the 3% punch to obtain a punch that is 20% pineapple juice?

Another Percent Mixture

One type of antifreeze is 40% glycol, and another type of antifreeze is 60% glycol. How much of each kind should be used to make 100 gallons of antifreeze that is 48% glycol?

Uniform Motion

Two trains are 550 miles apart heading towards each other on parallel tracks. Train A is traveling east at 35 miles per hour, while train B travels west at 45 miles per hour. When will the trains pass each other?

Another

Weighted Average