Bell Work: Be ready to hand in your signed course syllabus, and have your notebook out, open, and ready for notes!!!

Unit 1EQUATIONS AND INEQUALITIES

Unit Essential Question How do we translate real world applications of equations and inequalities into mathematical expressions?

Lesson 1.2EVALUATE AND SIMPLIFY ALGEBRAIC EXPRESSIONS

Lesson Essential Question (LEQ)How do we use the properties of real numbers to help us simplify algebraic expressions?

Evaluating Powers Examples:

1) Evaluate: and

2) Evaluate: and

3) Evaluate: and

PAY ATTENTION TO PARENTHESIS!!!

Evaluating Expressions Examples:

4) Evaluate if x = 3.

5) Evaluate if y = -2

Make sure you evaluate the powers first!!!

Combining Like Terms and Constants

Examples:

6) Simplify:

7) Simplify:

Remember: You can only combine terms if they have the same variable(s) raised to the same exponent!!!

Review Examples: 8) Evaluate

9) Evaluate

10) Simplify

11) Simplify

Homework: Pages 13 – 15 #’s 3-31 odds, 35, 41, 42, 50, 57, and 59

Bell Work: 1) Simplify:

2) Evaluate the simplified expression from number 1 if x = - 4

Lesson 1.3SOLVING LINEAR EQUATIONS

Lesson Essential Question (LEQ): How can we represent word problems as linear equations?

THE SUPER EASY ONES! Solve the following equations:

Examples:

1)

2)

3)

THE KINDA EASY ONES! Solve the following equations:

Examples:

4)

5)

6)

MEDIUM LEVEL EQUATIONS Solve the following equations:

Examples:

7)

8)

9)

Totally Sweet Equations: Solve the following equations:

Examples:

10)

11)

12)

Remember!!! It is possible for an equation to have:

NO SOLUTION, if the equation ends as a false statement.

Or

ALL REAL NUMBERS as the solution, if the equation ends as a true statement.

Extra Practice Problems… Solve the following equations.

13)

14)

Homework: Pages 21 – 23 #’s 11 – 25, 33 – 53, 63 – 67 odds only, then 68 – 71 all.

Bell Work: Solve the equations below.

1)

2)

3)

Bell Work Continued!!! 4) Levi and Emily sell luxury cars for a living. Levi has a base salary of $48,000 and earns 5% commission. Emily has a base salary of $64,000 and earns 3% commission. At what point will the two be earning the same amount?

5) It takes Trish 10 minutes to wash a car and it takes Jacob 12 minutes to wash a car. How long will it take the two of them to wash 22 cars if they work together???

Lesson 1.4REARRANGING FORMULAS AND EQUATIONS

Lesson Essential Question: Why is it necessary to rearrange a specific formula to solve for a different variable?

Important… Why would we want to rearrange formulas or equations?

Examples: 1) Solve for t.

2) Solve for h.

3) Solve for b.

Examples: 4) Solve for x.

5) Solve for y.

6) Solve for x.

Examples: 7) Solve for a.

8) Solve for y.

9) Solve for b.

10) Solve for x.

Homework: Pages 30-32 #’s 6, 7 – 25 odds, 28 – 32 all, 35, 37, and 39

Bell Work: 1) Solve.

2) Solve for x.

3) Solve for w.

Lesson 1.5PROBLEM SOLVING STRATEGIES

Lesson Essential Question: What are some of the strategies used to solve word problems?

Examples:1) A car used 16 gallons of gasoline and traveled a total distance of 460 miles.

The car’s fuel efficiency is 30 mpg highway and 25 mpg city. How many gallons of gasoline were used on the highway?

2) You are hanging four championship banners on the gym wall. The banners are 8 feet wide and the wall is 62 feet long. There needs to be an equal amount of space between the ends of the walls and the banners. How far apart should the banners be spaced?

Group Work: Pages 37 – 39 #’s 3 – 15 odds, 16 – 26 all, 29 – 31, 33

Bell Work: 1) Solve for x.

2) Solve for x.

3) Page 39 # 32

Bell Work: 1) The sum of three numbers is 126. The second number is four less than three times the first. The third number is five more than the second. Find the three numbers.

2) Write the formula for the area of a square in terms of its perimeter.

Examples: 3) Luke unloads 40 boxes from a truck that contains 8lb boxes of green beans and 5lb boxes of asparagus. If the total weight of the boxes he unloaded is 266lb, how many of each box did he unload?

Example: 4) The combined age of Mr. Kelsey, Mr. Kelsey’s father, and Mr. Kelsey’s grandfather is 176 years. His grandfather is three times as old Mr. Kelsey, and his father is 26 years older than Mr. Kelsey. Find each persons age.

Example: 5) You are laying tiles for a new bathroom floor. The tiles are 10 inches long, and the room is 11.375 feet long. You plan on laying 12 tiles, with equal space between each tile, but no space between the tiles next to the wall. What will be the space between each tile in terms of inches?

Example: 6) Kylan runs 24.5 miles in 3 hours and 30 minutes. He sprints for part of the race at 9 miles per hour and jogs part of the race at 2 miles per hour. How much time did he spend jogging?

How far did he travel while sprinting?

Example: 7) The combined weight of four wrestlers is 530 pounds. The second wrestler weighs 40lb more than the first. The third weighs 22 less than the second. The fourth weighs 8 less than the first. Find the weights of the four wrestlers.

Example: 8) Write the formula for the volume of a sphere in terms of its circumference.

9) Prove that the new formula is correct by find the volume of a sphere with a radius of 5cm using the new and original formula for volume.

10) Solve for x.

Example: 11) Write the formula for the area of a cube in terms of its surface area.

Quiz Tomorrow: The quiz will be on:

Evaluating Expressions

Combining Like Terms and Constants

Solving Equations

Rearranging Equations

Equation Word Problems

Bell Work: 1) What are the four main inequality symbols?

2) Why do we graph solutions for inequalities on a number line?

3) What is interval notation?

Lesson 1.6SOLVING LINEAR INEQUALITIES

Lesson Essential Question: What are inequalities, how do we solve them, and how do we represent the solutions?

Solving Linear Inequalities Examples on board…

Homework: Pages 45 – 47 #’s 25 – 51 odds 52, 53, 56, 60

Bell Work: Solve the inequality, graph the solution on a number line, and write the interval notation.

1)

Lesson 1.7ABSOLUTE VALUE EQUATIONS AND INEQUALITIES

Lesson Essential Question: What do the absolute value symbols do to an equation and inequality?

Absolute Value Equations If , then we can rewrite this as two separate equations:

1) 2)

Because absolute value shows the distance from zero on the number line, we have to remember that there are two sides of the number line, so it is possible to have two solutions for absolute value equations.

Extraneous Solutions/No Solutions

It is possible that one of the solutions you found does not work when substituted back into the original equation. These are called extraneous solutions. It is imperative that you check your work to insure that the answers you found work.

It is also possible that none of the solutions work. This will occur if the equation is set equal a negative number.

Homework: Page 55 #’s 3 – 41 odds

Bell Work: Pop Quiz: Grab a small piece of paper from the front of the room and begin.

1) Solve the inequality and write the interval notation.

2) Solve the absolute value equation.

Bell Work: Solve the following equations:

1)

2)

3)

Absolute Value Inequalities: BLUE TABLE ON PAGE 53!!!

You should memorize this!

Examples:

Homework: Page 56 #’s 43 – 65 odds

Bell Work: 1) You plan to buy 18 picture frames for your friends. 8x10 photo frames cost $10 each and 6x8 photo frames cost $7.50 each. If you want to spend at least $150 but no more than $175 for the 18 picture frames, write and solve an inequality to show the different possible combinations that you can purchase.

2) Emily wants to hang four pictures on her bedroom wall that is 12 feet and 1 inch long. Each picture that she hangs is 10 inches wide, the space between each picture needs to be the same, and the distance between the end pictures and the wall needs to be twice as much as between the pictures. What will be the space between each picture? What is the space between the end pictures and the walls?

Test on Thursday You need to know:

Evaluating Expressions and Combining Like Terms

Solving Equations (watch out for ARN/NS)

Solving Inequalities (Interval Notation as well)

Word Problems

Rearranging Equations/Formulas

Absolute Value Equations/Inequalities

Examples: Solve each absolute value equation:

1)

2)

3)

Examples: Solve the absolute value inequalities. Write the final inequalities in interval notation.

4)

5)

6)

Homework: This will be collected tomorrow! Pages 55 – 56 #’s 30 – 40 evens, 54 – 62 evens

Bell Work: 1) A single cup has a height of 6.5 inches. When another identical cup is stacked on top of it, the total height of the two cups is 9 inches. Write an equation to show the height of n cups. Use this equation to show the height of 25 cups in terms of feet and inches.

2) Solve.

3) Solve for x.

4) A piece of string 20 feet long is cut into 4 pieces. The first two pieces are the same length, the third piece is 8 inches longer than the first two, and the fourth piece is twice the length of the third. Find the length of the four pieces.

Bell Work: 1) Solve for y.

2) Solve.

3) Solve.

Word Problems: 4) Jane is driving from Pittsburgh to Watsontown. She drives the 300 miles in 5 hours. She was driving 75 mph on the highway and 25 mph in the city. How much time did she spend on the highway? What was the total distance she traveled on the highway?

5) The sum of three numbers is 400. The second number is half the first number, and the third number is 25 more than twice the second. Find the three numbers.

6) The height of 4 chairs stacked on each other is 4 feet 8 inches. The height of 9 chairs stacked is 8 feet 10 inches. Write an equation to show the height of n chairs. Use this equation to find the height of 15 chairs in terms of feet and inches.

Word Problems: 7) Five championship banners are being hung in the gymnasium. Each banner is 6 feet wide, and the space between each banner will be the same. The space between the end banners and the wall needs to be 8 feet more than the space between each banner. If the wall is 88 feet long, what will be the space between each banner?

8) Solve for a.

9) Solve.

Review Problems: 10) Solve.

11) Solve.

12) Solve.