College Algebra Course: MA178 College Algebra Year: Spring 2009 Date: Jan 12 Instructor: P Dorshorst...

College Algebra

• Course: MA178 College Algebra• Year: Spring 2009• Date: Jan 12• Instructor: P Dorshorst• Location: Oberlin• DO NOT CROSS ANYTHING OUT!!• Signature• Do NOT put SSN on the form

Meeting Dates

• M T W Th: Starting on Jan 12• Classtime: 4:00 – 5:00 p.m.• In the event that you miss class go to the

tutorial on school shared drive. After opening the appropriate Power Point slide show, select the “View Show” option under “Slide Show” on the task bar. Hit return to progress the slide show at your own rate. Come in sometime during the day to take your quiz.

Books: College Algebra (Seventh Edition, 2005)

ISBN: 0-13-143092-0Author: Sullivan

Pearson Prentice Hall• Students that may have used books• Adrienne Pauls• Stephanie Bruggeman• Fredrickson, Jessica• Fredrickson, Sunnie JO• May, Cole• Meitl, Kyra• Rittman, Christian• Benke, Whitney

Linear Equations

Equation: Statement in which two expressions, at least one

containing a variable, are equal.

Solution or Root

• Values of the variable, if any, that result in a true statement.

• To SOLVE an equation means to find all possible solutions of the equation.

• An IDENTITY is an equation that every value of the variable makes a true statement.

Process of Solving Equations• Linear: 3(x – 2) + 5 = 2x – 4

– Simplify each side of the equation3x – 6 + 5 = 2x – 4 distribute 33x – 1 = 2x – 4 combine like terms– Move variables to the same side by

adding/subtracting– 3x – 2x – 1 = 2x – 2x – 4 -> x – 1 = -4– Move numbers away from the variable

• Add/Subtract first • X – 1 + 1 = - 4 + 1 -> x = - 3• Then multiply/divide

– Check your answer/s – 3(-3 – 2) + 5 = 2(-3) – 4 -> -15 + 5 = -6 - 4

Examples

• Solve 3x – 5 = 4– Simplify each side of the equation – Move variables to the same side by

adding/subtracting– Move numbers away from the variable

• Add/Subtract first • 3x – 5 + 5 = 4 + 5 -> 3x = 9 • Then multiply/divide• 3x / 3 = 9 / 3 -> x = 3

– Check your answer/s

Solve 3 + 2n = 4n + 7

– Simplify each side of the equation – Move variables to the same side by

adding/subtracting– 3 + 2n – 2n = 4n – 2n + 7 -> 3 = 2n + 7– Move numbers away from the variable

• Add/Subtract first 3 – 7 = 2n + 7 – 7 -> - 4 = 2n• Then multiply/divide- 4 / 2 = 2n / 2 -> -2 = n

– Check your answer/s– 3 + 2(-2) = 4(-2) + 7 -> -1 = -1

Solve 2p/3 = 1p/2 + 1/3

• Multiply both sides of equation by the common denominator to eliminate the fractions (Multiplicative Property of Equality)

• 6(2p/3) = 6(1p/2) + 6(1/3)• Reduce the denominator and solve• 4p = 3p + 2• 4p – 3p = 3p – 3p + 2• P = 2

x / (x – 2) + 3 = 2 / (x – 2)

• Multiply by the common denominator to simplify the equation

• (x – 2) (x/(x – 2)) + 3(x – 2) = (x – 2)(2/(x – 2))• Reduce out denominators: X + 3x – 6 = 2• 4x – 6 = 2• 4x = 8• X = 2• 2 does not check in the original (causes an

undefined value in denominator) so “no solution”

Try each of these examples on your own. After completing the problem hit enter to check your answer. If you do not get the correct answer

please contact me for help.• ½ (x + 5) – 4 = 1/3 (2x – 1)• X = - 7• 2.78x + 2 / 17.931 = 54.06• X = 19.41• (2y + 1)(y – 1) = (y + 5)(2y – 5)• X = 4• 3x / (x -1) + 2 = 3 / (x -1)• X = No Solution

Applications

1. Read through the problem carefully (more than once helps). Pay particular attention to the question being asked – this is generally your variable.

2. Assign a variable to represent what you are looking for and if necessary express any other unknown quantities in terms of the variable.

3. Make a list of all known facts, and translate them into mathematical expressions. (Sometimes a labeled diagram or a table of information helps to distinguish relationships.)

4. Write an equation and solve.

5. Check answer/s with facts in problem.

Examples

• In the United States we measure temperature in both degrees Fahrenheit and degrees Celsius, which are related by the formula C = 5/9 (F – 32). What are the degrees Fahrenheit temperatures corresponding to Celsius temperatures of 0o, 10o, 20o, and 30o C?

• (It may help to solve the equation for F before starting.) After solving for F hit return.

• 9C = 5(F – 32) multiply both sides by 9• 9C = 5F – 160 distribute the 5• 9C + 160 = 5F add 160• 9/5 C + 32 = F divide by 5

• Substitute each value in for C and find the related value for F

• 0o C = 32oF 10oC = 50oF• 20o C = 68oF 30oC = 86oF

• A total of $18,000 is invested, some in stocks and some in bonds. If the amount invested in bonds is half that invested in stocks, how much is invested in each category?

• Describe each of the two investments• X 18,000 – x since the two

combine to 18,000

• A total of $18,000 is invested, some in stocks and some in bonds. If the amount invested in bonds is half that invested in stocks, how much is invested in each category?

• Total in bonds is ½ that in stocks

• 18,000 – x = ½(x)

Solve: 18,000 – x = ½ x

• Multiply by 2 to eliminate fraction

• 2(18,000) – 2(x) = 2(1/2)x

• 36,000 – 2x = x

• 36,000 = 3x

• 12,000 = x

• 18,000 – 12,000 = 6,000

• $12,000 in stocks; $6,000 in bonds

After trying the following problem hit return to check your answer. If you do not get the correct

answer please see Mrs. Dorshorst for help.• A total of $20,000 is to be invested, some

ion bonds and some in certificates of deposit (CDs). If the amount invested in bonds is to exceed that in CDs by $3000, how much will be invested in each type of investment?

• $11,500 in bonds; $8500 in CDs

Write the equation then hit return to check your work.

• Shannon grossed $435 one week by working 52 hours. Her employer pays time-and-a-half for all hours worked in excess of 40 hours. With this information, can you determine Shannon’s regular hourly wage?

• Let x equal the regular hourly wage• 40x: regular wage• 12 (1.5x): overtime wage• 40x + 12(1.5x) = 435

40x + 12(1.5x) = 435

• 40x + 18x = 435

• 58x = 435

• X = $7.50

Assignment:

• Page 94

• #21, 27, 33, 41, 43, 53, 63, 77, 81, 85, 87, 91, 95, 97