Transcript College Algebra - Oberlin USD 294

College Algebra
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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.
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Books: College Algebra (Seventh Edition,
2005)
ISBN: 0-13-143092-0
Author: 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 equation
3x – 6 + 5 = 2x – 4 distribute 3
3x – 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 ->
• Then multiply/divide
x=-3
– 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
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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 ->
• Then multiply/divide
- 4 / 2 = 2n / 2
->
– Check your answer/s
– 3 + 2(-2) = 4(-2) + 7
- 4 = 2n
-2 = n
->
-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))
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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
contact
• ½ (x + 5) – 4please
= 1/3 (2x
– 1) me for help.
• 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.
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9C = 5(F – 32)
9C = 5F – 160
9C + 160 = 5F
9/5 C + 32 = F
multiply both sides by 9
distribute the 5
add 160
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
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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
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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