Algebra I Chapter 2 Section 1 Solving Equations by Adding and Subtracting

Algebra I chapter 2 section 1 solving equations by adding and subtracting

Warm-up

Evaluate

-0.51 + (-0.29)

Give the opposite of each number

8

-2/3

Evaluate each expression for a = 3 and b = -2

a + 5

12 – b

An ______is a mathematical statement that two expressions are equal.

A ______is a value of the variable that make the equation true.,

To find solutions, ______the variable.

An equation is like a balanced scale. To keep the balance, perform the same operation on both sides.

INVERSE OPERATIONS

Properties of equality

Solve each equation. YOU MUST SHOW ALL WORK AND CHECK YOUR ANSWERS

x – 10 = 42/5 = m – 1/5

Solve each equation. YOU MUST SHOW ALL WORK AND CHECK YOUR ANSWERS

N – 3.2 = 5.6-6 = k – 6

16 = m – 9x + 7 =9

0.7 = x + 0.4d + ½ = 1

-5 = K + 56 + x = 14

-8 + x = 2-2.3 + x = 7

-3/4 + z = 5/4-11 + x = 33

Homework 2.1 pg 80 #21-40, 51-57, 58, 60, 66, 68, 69

Algebra I Chapter 2 Section 2 solving equations by multiplying or dividing

Warm up

Evaluate each expression

(-7)(2.8)

0.96 ÷6

(-9)(-9)

(5/6)(6/5)

(3/4)(2.4)

Solving an equation that contains multiplication or division is similar to solving an equation that contains ______or ______. Use ______operations to undo the operations on the variable.

REMEMBER: An equation is like a balanced scale. To keep the balance, perform the same operation on both sides.

Solve each equation. You must show all your work and check your answers.

=1.5

7x + 56

16 = 4x

0.5y = -10

15k = 75

9y = 108

-4.8 = -6

PROPERTIES OF EQUALTIY

Homework 2.2 pg 87 # 21-46, 48-54 even, 56-64, 66-74 even, 77-80, 96-104 even

Algebra I Chapter 2 section 3 solving two-step and multi step equations

Warm-up

Evaluate each expression

9 – 3(-2)

3(-5 + 7)

26 – 4(7 - 5)

Simplify each expression

10x + x

8.2b +3.8b – 12b

5m + 2(2m – 7)

6x –(2x + 5)

Solve each equation. You must show all your work and check your answers.

10 = 6 – 2x-4 + 7x = 3

1.5 = 1.2y – 5.7n/7 + 2 = 2

18 = 4a + 105x – 2 = -32

METHOD 1 METHOD 2

6x + 3 – 8x = 138x – 21 – 5x = -15

10y – (4y + 8) = -209 = 6 – (x + 2)

Homework 2.3 pg 96 # 1 - 23

Algebra I Chapter 2 Section 3 part 2

Solve each equation. You must show all your work and check your answers.

2a + 3 – 8a = 8-2(3 – d) = 4

4(x – 2) + 2x = 40

Jan joined the dining club at the local café for a fee of $29.95. Being a member entitles her to save $2.50 every time she buys lunch. So far, Jan calculates that she has saved a total of $12.25 by joining the club. WRITE and SOLVE an equation to find how many times Jan has eaten lunch at the café.

If 3a + 12 = 30, find the value of a + 4

If 4a + 0.2 = 5, find the value of a – 1

If 3d – (9 – 2d) = 51, find the value of 3d

Homework 2.3 pt 2 page 96 # 24-46 even, 50 – 52, 54-66 even, 70-72, 82 – 92 even

Algebra I Chapter 2 Section 4 Solving equations with variables on both sides

Warm up

Simplify

4x – 10x

-7(x – 3)

1/3(6x + 9)

15 – (x – 2)

SOLVE

3x + 2 = 8

1/3x – 1/3 = 9

TO solve an equation with variables on both sides, use inverse operation to “______” variable terms on one side of the equation.

Solve each equation. You must show all your work and check your answers.

7x = 4x + 154x + 2 = 3x

0.5 + 0.3y = 0.7y – 0.37x – 2 = 5x + 6

2(y + 6) = 3y3 – 5x + 2x = -2 -2(1 – x)

3x + 15 – 9 = 2(x + 2)

An ______is an equation that is true for all values of the variable. An equation that is an ______has infinitely many solutions. A ______is a equation that is not true for any value of the variable. Is has ______solutions.

10 – 5x + 1 = 7x + 11 – 12x12x – 3 + x = 5x – 4 + 8x

4y + 7 – y = 10 + 3y2x + 7 + x = -14 + 3x + 21

Homework 2.4 Pg 103 #16- 50 even, 58-61, 72 – 84 even

Algebra I chapter 2 Section 5 Solving for a Variable

Warm-up

Solve each equation

5 + x = -28m = 43

(c+5)/4 = 60.3x +0.6 = 1.5

10x – 6 = 9x + 2

A ______is an equation that states a rule for a relationship among quantities.

In the formula d = rt, d is isolated. This is called solving for a ______.

Solve for a variable

Solve the formula d = rt for t. Find the time in hours that it would take Van Dyk to travel 26.2 miles if his average speed was 18 miles per hour.

The formula for an object’s final velocity f is f = i – gt, where I is the object’s initial velocity, g is acceleration due to gravity and t is time. Solve for i.

The formula C =d give the circumference of a circle C in terms of its diameter. Solve the equation for d. If the circumference of a bowl is 18 inches, what is the bowl’s diameter? Leave the answer in terms of .

The formula for the area of a triangle is ______. Solve for h.

Solve the formula for a person’s typing speed for e.

A ______is an equation with two or more variables. To solve for one of the variables, use ______.

Solve x + y = 15 for x

Solve pq = x for q

Solve 5 – b = 2t for t

Solve D = M/V for V

Homework 2-5 Pg 109 # 8-13, 14-28even, 35-37, 46-54 evens

Algebra I Chapter 2 Section 6 Rates, Ratios and Proportions

Warm up

Solve each equation.

6x = 36x/4 = 12

5m = 18x/21 = -3

r/21 = -38y = 18.4

A ______is a comparison of two quantities by division. It can be written as ______or ______

They are said to be equivalent if ______.

A statement that two ratios are equivalent is called a ______.

A ______is a ratio of two quantities with different units. A ______is a rate with a second quantity of 1 unit . You can convert any rate to a unit rate.

The ratio of games won to games lost for a baseball team is 3:2. The team won 18 games. How many games did they lose?

Cory earns $52.50 in 7 hours. Find the unit rate.

The ratio of the number of bones in the human skull to the number of bones in the ears is 11:3. There are 22 bones in the skull. How many bones are in the ear?

Ralf Laue of Germany flipped a pancake 416 times in 120 seconds to set the world record. Find the unit rate. Round your answer to the nearest hundredth.

A cyclist travels 56 miles in 4 hours. What is the cyclist’s speed in feet per second? Round your answer to the nearest tenth.

A cheetah can run at a rate of 60 mph is short bursts. What s this speed in feet per minute?

Cross Products Property

You can solve proportion for a missing value by using the cross product property.

Solve each proportion

A______is a ratio between two sets of measurements, such as 1 in : 5 mi. A ______or ______uses a scale to represent an object as smaller or larger than the actual object. A map is an example of a scale drawing.

On a map, the distance from Chicago to Evanston is 0.625 in. If the scale is 1 in: 18 mi., what is the actual distance.

The actual distance between North Chicago and Waukegan is 4 mi. What is this distance on the map? Round to the nearest tenth. (the scale is 1 in: 18 mi)

A scale model of a human heart is 16 ft long. The scale is 32:1. How many inches long is the actual heart it represents?

A contractor has a blueprint for a house drawn to the scale 1 in : 3 ft.

A wall on the blueprint is 6.5 inches long. How long is the actual wall?

One wall of the house will be 12 feet long when it is build. How long is the wall on the blueprint?

Homework 2.6 pg 117 #20-38 even, 44-54 even, 59-62, 66-78 even

Algebra I Chapter 2 Section 7 Applications of proportions

Warm-up

Evaluate each expression for a = 3, b = -2 and c = 5

4a – b3b² - 5

ab – 2c

Solve each proportion

______figures have exactly the same shape but not necessarily the same size.

______of two figures are in the same relative position and ______are in the same relative position. Two figures are similar if and only if the lengths of corresponding sides are proportional and all parts of corresponding angles have equal measures.

Find the value of x in each diagram.

Find the value of x in each diagram

A flagpole casts a shadow that is 75 ft long at the same time a 6 foot tall man casts a shadow that is 9 ft long. Write and solve a proportion to find the height of the flag pole.

A forest ranger who is 150 cm tall casts a shadow 45 cm long. At the same time a nearby tree casts a shadow 195 cm long. Write ad solve a proportion to find the height of the tree.

A woman who is 5.5 feet tall casts a shadow 3.5 feet long. At the same time, a telephone pole casts a shadow 28 feet long. Write and solve a proportion to fin d the height of the telephone pole.

If every dimension of a figure is multiplied by the same number, the results is a similar figure. The multiplier is called a ______.

Every dimension of a 2 by 4 inch rectangle is multiplied by 1.5 to form a similar rectangle. How is the ratio of the perimeters related to the ratio of corresponding sides? How is the ratio of the areas related to the ratio of corresponding sides?

A rectangle has width 12 inches and length 3 inches. Every dimension of the rectangle is multiplied by 1/3 to form a similar rectangle. How is the ratio of the perimeters related to the ratio of the corresponding sides?

The radius of a circle with radius 8 in is multiplied by 1.75 to get a circle with radius 14 in. How is the ratio of the circumferences related to the ratio of the radii? How is the areas related to the ratio of the radii?

Every dimension of a rectangular prism with length 12 cm, width 3 cm and height 9 cm is multiplied by 1/3 to get a similar rectangular prism. How is the volumes related to the ratio of the corresponding dimensions?

Homework 2.7 pg 124 # 6-13, 14-18 even, 21-27, 30-40 even

Algebra I Chapter 2 Section 8 Percents

Warm up

Change each percent to a decimal

73%112%0.6%1%

Change each fraction or mixed number to a decimal

½ ⅓⅘1⅕

Solve each proportion

A ______is a ratio that compares a number to 100.

Some Common Equivalents

You can use the proportion to find unknown values.

Find 50% of 20.Find 20% of 60

Find 210% of 8Find 4% of 32

Find 30% of 8027 is what percent of 9

What percent of 45 is 35? Round your answer to the nearest tenth.

230 is what percent of 200?

38% of what number is 85? Round your answer to the nearest tenth

20 is 0.4% of what number

The serving size of a popular orange drink is 12 oz. The drink is advertised as containing 5% orange juice. How many ounces of orange juice are in one serving size?

Jewelers use the karat system to determine the amount of pure gold in jewelry. Pure gold is 24 karat, meaning the item is 100% gold. A 14 karat gold ring contains 14 parts gold and 10 parts other metal. What percent of the ring is gold?

Homework 2-8 Pg 130 #15-27, 28-46 even, 50-55, 60-64, 71-77

Algebra I Chapter 2 section 9 Applications of percents

Warm up

Write 0.03 as a percent

Write 4½ % as a decimal

Find each value

Find 10% of 53

Find 2½ % of 50

A ______is mone paid to a person or a company for making a sale.

A telemarketer earns $350 per week plus 12% commission on sales. Find her total pay for a week in which her sales are $940.

Mr. Cortez earns a base salary of $26,000 plus a sales commission of 5%. His total sales for one year were $300,000. Find his total pay for the year.

______is the amount of money charged for borrowing money, or the amount of money earned when salving or investing money. ______is the amount borrowed or invested.

Simple interest is interest paid only on the principal. I = PRT

Find the simple interest paid annually for 3 years on a $2500 loan at 11.5% per year.

Find the simple interest earned after 2 years on an investment of $3000 at 4.5% interest earned annually

The simple interest paid on a loan after 6 months was $300. The annual interest rate was 8%. Find the principal.

A ______is an amount of money added to a bill for service. It is usually a percent of the bill. ______is a percent of an item’s cost.

Lunch at a restaurant is $27.88. Estimate a 15% tip

Estimate a 15%tip on a check for $21.98

The sales tax rate is 7.25%. Estimate the sales tax on a book that costs $19.97

Estimate the tax on shoes that cost $68.50 when the sales tax rate is 8.25%

Homework 2.9 pg 135 #9-14, 16-22, 27, 28, 35-43

Algebra I chapter 2 Section 10 Percent Increase and Decrease

Warm up

Find 30% of 40Find 28% of 60

Solve for x

22 = 50x17.2 = 86x

20 is what percent of 80?36 is what percent of 30?

A ______is a increase or decrease given as a percent of the original amount. ______describes an amount that has grown and ______describes an amount that has been reduced.

Find each percent change. Tell whether it is a percent increase or decrease

From 200 to 110from 25 to 30

From 80 to 115from 75 to 30

Find the result when 72 is increased b 25%

Find the result when 12 is increased by 50%

Find the result when 55 is decreased by 60%

A $220 bicycle was on sale for 60% off. Find the sale price

Ray paid $12 for a $15 t-shirt. What was the percent discount?

The entrance fee at an amusement park is $35. People over the age of 65 receive a 20% discount. What is the amount of the discount? How much do people over 65 pay?

A student pair $31.50 for art supplies that normally cost $52.00 Find the percent discount.

The wholesale cost of a DVD is $7. The markup is 85%. What is the amount of the markup? What is the selling price?

A video game has a 70% markup. The wholesale cost is $9. What is the selling price?

What is the percent markup on a car selling for $21,850 that had a wholesale cost of $9500

Homework 2-10 Pg 141 #16-35, 37-40, 45-47, 52-55, 64-76 even