Welcome to our seminar. We will begin at 2:30 PM. **You will need a pen or pencil and some paper** You can get a calculator, too. MM150 Seminar Unit 3: Algebra with Professor Golden

W ELCOME TO MM150 S EMINAR 1 -- If you are not in my class and would like a copy of these seminar slides, please me and I will send them to you. -- If you are in my class, there are copies of my seminars in Doc Sharing Office Hours on AIM: ProfGoldenKaplan Tuesdays: 6:00 – 7:00 PM and Wednesdays: 11:00 AM- 12:00 PM -- SEMINAR: Mondays, 2:30 AM – 3:30 PM ( 5 points) or Seminar 2 Quiz -- Reading each week(video lectures, too) --MyMathLab(MML) 20 homework problems each week (60 points) Kaplan help desk: Due each week on Tuesday by 11:59 PM (Locks out) --Discussion Board: Three mathematical postings EACH week (30 points) -- Final Project: Due at end of term, Dec. 15 (145 points)

The white part of your fingernail is called the lunula.

Emus cannot walk backwards

Cats have over one hundred vocal sounds, while dogs only have about ten.

Which is the only planet in our solar system that rotates in a different direction from the other planets?

D EFINITIONS Algebra: a generalized form of arithmetic. Variables: letters used to represent numbers Constant: symbol that represents a specific quantity (numbers) Algebraic expression: a collection of variables, numbers, parentheses, and operation symbols. Examples:

T HE O RDER OF O PERATIONS (PEMDAS) Please Excuse My Dear Aunt Sally P( Parentheses) E( Exponents) M( Multiplication) D(Division) A(Addition) S(Subtraction) **This is the order that you must do all calculations** PLEASE NOTE, once you are down to all multiplication/division or all addition/subtraction, you work these in order from LEFT to RIGHT.

Simplify: 2³ ÷ You must follow the PEMDAS order of operations: First work inside parentheses Next do exponents Next do multiplication: Next do division : Next addition and subtraction F OR E XAMPLE :

Simplify: 2 x 5 ÷ 2 x 1 Simplify:

E VALUATING AN E XPRESSION Evaluate the expression x 2 + 4x + 5 for x = 3. Solution: x 2 + 4x + 5 = (3) + 5 = = 26

E XAMPLE : S UBSTITUTING FOR T WO V ARIABLES Evaluate when x = 3 and y = 4.

Evaluate : -3x² - 2x - 4 for x = -2

S ECTION 3.2 Terms are parts that are added or subtracted in an algebraic expression. Coefficient is the numerical part of a term. Like terms are terms that have the same variables with the same exponents on the variables. Unlike terms have different variables or different exponents on the variables.

P ROPERTIES OF THE R EAL N UMBERS Associative property of multiplication (ab)c = a(bc) Associative property of addition (a + b) + c = a + (b + c) Commutative property of multiplication ab = ba Commutative property of addition a + b = b + a Distributive propertya(b + c) = ab + ac

E XAMPLE : C OMBINE L IKE T ERMS 8x + 4x = (8 + 4)x = 12x 5y  6y = (5  6)y =  y x + 15  5x + 9 = (1  5)x + (15 + 9) =  4x x y  4 + 7x = (3 + 7)x + 6y + (2  4) = 10x + 6y  2

S OLVING E QUATIONS Addition Property of Equality If a = b, then a + c = b + c for all real numbers a, b, and c. Find the solution to the equation x  9 = 24. x  = x = 33 Check: x  9 =  9 = 24 ? 24 = 24 true

Find the solution to the equation x - 12 = 36

S OLVING E QUATIONS CONTINUED Subtraction Property of Equality If a = b, then a  c = b  c for all real numbers a, b, and c. Find the solution to the equation x + 12 = 31. x + 12  12 = 31  12 x = 19 Check: x + 12 = = 31 ? 31 = 31 true

Find the solution to the equation x + 12 = 36

S OLVING E QUATIONS CONTINUED Division Property of Equality If a = b, then for all real numbers a, b, and c, c  0. Find the solution to the equation 4x = 48.

Find the solution to the equation -4x = 16. Find the solution to the equation 5x = 30

S OLVING E QUATIONS CONTINUED Multiplication Property of Equality If a = b, then a c = b c for all real numbers a, b, and c, where c  0. Find the solution to the equation

Find the solution to: x = 6 4

E XAMPLE : S OLVING E QUATIONS Solve 3x  4 = 17.

Solve 4x  4 = 16

E XAMPLE : S OLVING E QUATIONS Solve 21 = 6 + 3(x + 2).

Solve 34 = (3x + 2)

E XAMPLE : S OLVING E QUATIONS Solve 8x + 3 = 6x + 21.

Solve 6x + 4 = 2x + 16.

P ROPORTIONS A proportion is a statement of equality between two ratios. Cross Multiplication If then ad = bc, b  0, d  0.

E XAMPLE A 50 pound bag of fertilizer will cover an area of 15,000 ft 2. How many pounds are needed to cover an area of 226,000 ft 2 ? 754 pounds of fertilizer would be needed.

If a 2 pounds of ground beef costs $5.12, how much will it cost to buy 5 pounds of ground beef?

S ECTION 3.3 F ORMULAS A formula is an equation that typically has a real-life application. To evaluate a formula, substitute the given value for their respective variables and then evaluate using the order of operations.

P ERIMETER The formula for the perimeter of a rectangle is Perimeter = 2 length + 2 width or P = 2l + 2w. Use the formula to find the perimeter of a yard when l = 150 feet and w = 100 feet. P = 2l + 2w P = 2(150) + 2(100) P = P = 500 feet

E XAMPLE The formula for the volume of a cylinder is V =  r 2 h. Use the formula to find the height of a cylinder with a radius of 6 inches and a volume of in 3. The height of the cylinder is 5 inches.

S OLVING FOR A V ARIABLE IN A F ORMULA OR E QUATION Solve the equation 3x + 8y  9 = 0 for y.

T RANSLATING W ORDS TO E XPRESSIONS 2x2x Twice a number x – 8 A number decreased by 8 x – 4Four less than a number x + 5A number increased by 5 x + 10Ten more than a number Mathematical Expression Phrase Section 3.4 Applications of Linear Equations

T RANSLATING W ORDS TO E XPRESSIONS Five less than 7 times a number x – 6 The difference between a number and 6 2 – x 2 decreased by a number 4x4xFour times a number Mathematical Expression Phrase 7x – 5

T RANSLATING W ORDS TO E XPRESSIONS 2x  3 = 8 Twice a number, decreased by 3 is 8. x – 3 = 4 Three less than a number is 4 x + 7 = 12 Seven more than a number is 12 Mathematical Equation Phrase x  15 = 9x A number decreased by 15 is 9 times the number

T O S OLVE A W ORD P ROBLEM Read the problem carefully at least twice to be sure that you understand it. If possible, draw a sketch to help visualize the problem. Determine which quantity you are being asked to find. Choose a letter to represent this unknown quantity. Write down exactly what this letter represents. Write the word problem as an equation. Solve the equation for the unknown quantity. Answer the question or questions asked. Check the solution.

E XAMPLE The bill (parts and labor) for the repairs of a car was $ The cost of the parts was $339. The cost of the labor was $45 per hour. How many hours were billed? Let h = the number of hours billed Cost of parts + labor = total amount h =

How many eggs can you put in an empty basket?