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

WELCOME TO MM150 SEMINAR 1-- If you are not in my class and would like a copy of these seminar slides, please email me and I will send them to you.-- If you are in my class, there are copies of my seminars in Doc Sharing.--Email: agolden@kaplan.edu--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: 1- 866-522-7747 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?

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

THE ORDER OF OPERATIONS (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: 2 2 + 1 4 You must follow the PEMDAS order of operations: First work inside parenthesesNext do exponentsNext do multiplication:Next do division :Next addition and subtraction

FOR EXAMPLE:

Simplify: 2 x 5 2 x 1

Simplify: 12 - 3 + 4 - 8

EVALUATING AN EXPRESSIONEvaluate the expression x2 + 4x + 5 for x = 3.

Solution: x2 + 4x + 5 = 32 + 4(3) + 5 = 9 + 12 + 5 = 26

EXAMPLE: SUBSTITUTING FOR TWO VARIABLESEvaluate when x = 3 and y = 4.

Evaluate : -3x - 2x - 4 for x = -2

SECTION 3.2Terms 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.

PROPERTIES OF THE REAL NUMBERS

EXAMPLE: COMBINE LIKE TERMS8x + 4x= (8 + 4)x= 12x

5y 6y= (5 6)y= y

x + 15 5x + 9= (1 5)x + (15 + 9)= 4x + 24

3x + 2 + 6y 4 + 7x = (3 + 7)x + 6y + (2 4)= 10x + 6y 2

SOLVING EQUATIONSAddition 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 9 + 9 = 24 + 9 x = 33 Check: x 9 = 24 33 9 = 24 ? 24 = 24 true

Find the solution to the equation x - 12 = 36

SOLVING EQUATIONS CONTINUEDSubtraction 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 19 + 12 = 31 ? 31 = 31 true

Find the solution to the equation x + 12 = 36

SOLVING EQUATIONS CONTINUEDDivision 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

SOLVING EQUATIONS CONTINUEDMultiplication 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

EXAMPLE: SOLVING EQUATIONSSolve 3x 4 = 17.

Solve 4x 4 = 16

EXAMPLE: SOLVING EQUATIONSSolve 21 = 6 + 3(x + 2) .

Solve 34 = 2 + 4 (3x + 2)

EXAMPLE: SOLVING EQUATIONSSolve 8x + 3 = 6x + 21.

Solve 6x + 4 = 2x + 16.

PROPORTIONSA proportion is a statement of equality between two ratios.

Cross Multiplication

If then ad = bc, b 0, d 0.

EXAMPLEA 50 pound bag of fertilizer will cover an area of 15,000 ft2. How many pounds are needed to cover an area of 226,000 ft2?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?

SECTION 3.3 FORMULASA 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.

PERIMETERThe 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 + 2wP = 2(150) + 2(100)P = 300 + 200P = 500 feet

EXAMPLEThe formula for the volume of a cylinder is V = r2h. Use the formula to find the height of a cylinder with a radius of 6 inches and a volume of 565.49 in3.

The height of the cylinder is 5 inches.

SOLVING FOR A VARIABLE IN A FORMULA OR EQUATIONSolve the equation 3x + 8y 9 = 0 for y.

TRANSLATING WORDS TO EXPRESSIONS2xTwice a numberx 8A number decreased by 8x 4Four less than a numberx + 5A number increased by 5x + 10Ten more than a numberMathematical ExpressionPhraseSection 3.4 Applications of Linear Equations

TRANSLATING WORDS TO EXPRESSIONSFive less than 7 times a numberx 6The difference between a number and 62 x2 decreased by a number4xFour times a numberMathematical ExpressionPhrase7x 5

TRANSLATING WORDS TO EXPRESSIONS2x 3 = 8Twice a number, decreased by 3 is 8.x 3 = 4Three less than a number is 4x + 7 = 12Seven more than a number is 12Mathematical EquationPhrasex 15 = 9xA number decreased by 15 is 9 times the number

TO SOLVE A WORD PROBLEMRead 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.

EXAMPLEThe bill (parts and labor) for the repairs of a car was $496.50. 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 billedCost of parts + labor = total amount 339 + 45h = 496.50

How many eggs can you put in an empty basket?

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