Download MAT 1033C Week 1 Handout

Week 1 Handout
MAT 1033C
Professor Niraj Wagh J
Section 2.1 Linear Equations in One Variable
Linear Equations in One Variable
A linear equation in one variable is an equation that can be written in the form:
ax + b = c
where a, b, and c are real numbers and a ≠ 0. For example,
3x = 15,
7 – y = 3y,
4n – 9n + 6 = 0
are all times of linear equations in one variable.
When you SOLVE an equation you find the SOLUTION to the equation. That is
you find a number that when substituted into the equation makes both the right
hand side and left hand side of an equation equal.
Let’s examine this…
Our equation is:
3x + 4 = 7
-> ISOLATE the “X” term
3x + 4 = 7
−4 −4
-> All X’s on one side, everything else on the other!
3x = 3
-> Make the coefficient of “x” become 1 so divide 3 on both sides.
-> Thus, the solution is
x =1
-> Check by substituting the value into the original equation:
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3x 3
=
3 3
3(1) + 4 = 7
7 = 7, YES!
J
Review on Fractions & Lowest Common Denominator (LCD)
Suppose we are trying to add or subtract TWO fractions with DIFFERENT
denominators, can we do this automatically? NO! L
We must get both fractions to have the same denominator, we call this the lowest
common denominator (LCD). Once they have the same denominator, we can
add/subtract them!
For example,
I want to add:
1 3
+
2 5
We must find a number that 2 and 5 both go into because we want the denominator
to be the same! If it’s not the same we can’t add the two fractions!
What is the LCD? It is ____!
Why? ___ is the least common multiple (LCM) that 2 and 5 both go into.
____ x ____ = 10
When doing this we multiply BOTH the top and bottom of the fraction:
=
, we are completely simplified!
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2.1 Examples
Solve each equation and check.
1. -2x = 18
2. 5y – 3 = 11 + 3y
3. 4x + 14 = 6x + 8
4. 2(4x + 3) = 7x + 5
x x 5
6. + = 2 5 4
7. 1
1
1
5. x +1 = x +
4
6
2
2 + h h −1 1
+
= 9
3
3
That’s it for 2.1! W ork on MML 2.1. If you have ANY questions, please feel
free to ask! Intermediate Algebra is a hard course and I would love to help
you! J
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Section 2.2 An Introduction to Problem Solving
In this section we are going to talk about applications, i.e. story problems. Most
students find these problems to be very difficult but I will do my best to make sure
it’s as doable as possible. Throughout this course we are going to see a variety of
applications both here and in your lab.
General Steps to Solving Story Problems
1. Read the re-read problem.
2. State what you KNOW and what you want to FIND out.
-> Sometimes it’s helpful to draw a sketch of what the problem is asking.
3. Translate the problem into a mathematical equation.
4. Solve the equation.
5. Explain what your solution means.
2.2 Examples
Write the following as algebraic expressions. Then simplify.
1. The perimeter of a rectangle with length x and width x – 5.
2. The sum of three consecutive integers if the first is “z.”
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Solve.
3. Daytona International Speedway in Florida has 37,000 more grandstand seats
than twice the number of grandstand seats at the Darlington Motor Raceway in
South Carolina. Together, these two race tracks seat 220,000 NASCAR fans. How
many seats does each race track have?
That’s it for 2.2! W ork on MML 2.2. If you have ANY questions, please feel
free to ask! Intermediate Algebra is a hard course and I would love to help
you! J
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Section 2.3 Formulas & Problem Solving
This section is pretty similar to section 2.1. In 2.1., we solved linear equations, and in this
section we will be solving for particular variables of formulas.
Some general formulas:
I = PRT Interest = principal •rate •time
A = lw Area of a rec tan gle = length • width
d = rt Dis tan ce = rate •time
C = 2π r Circumfrence of a circle = 2 • π •radius
V = lwh Volume of a rec tan gular solid = length • width • height
nt
! r$
A = P #1+ & Compound Interest Formula : P = principal amount, r = rate, " n%
n = # of times compounded per year, t = time in years When you want to solve for a particular variable, the same general steps from 2.1
apply. Our goal is to isolate the variable that we want to solve for.
2.3 Examples
Solve each equation for the specified variable
1. Solve I = PRT for R
2. Solve P = 2L + 2W for W
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3. Solve A = Prt + P for P
4. Solve E = I(r + R) for r
5. Complete the table and find the balance A if $5000 is invested at an annual
percentage rate of 6% for 15 years and compounded n times per year.
n
A
1
2
4
12
365
2.3 is complete! W ork on MML 2.3. If you have ANY questions, please feel
free to ask! Intermediate Algebra is a hard course and I would love to help
you! J
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