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Wetzel
Math 101
2.1 & 2.2 – Linear Equations
What is an expression?
( does not have an = )
 Def. –
 Can simplify using PEMDAS
What is an equation?



( has an = )
Def. –
Can solve
You can +, –, • , and ÷ to one side of an equation as long as you do the
same thing to the other side of the equation.
What is a linear equation? ( all variables have an exponent of one )
Def. To Solve:
1.) Simplify each side of the equation.
2.) Get the variables you are solving for on one side of the equation.
3.) Isolate the variable by using PEMDAS backwards.
4.) Check the answer!
Example:
1.) x – 4 = 7
3.)
5
x  15
6
5.) 5t + 72 +8t = 17t – 28 + 11t
2.) 8x = 56
4.) 3m – 11 = 9m + 5
6.) -7 + 6n + 21 = 28 + 6n
7.) P = a + b + 2c; solve for c.
EXTRA PRACTICE.
1.) 18  8  6b
3.) 2(3n  1)  4n  2  2n
5.) 13(3x  4)  7(2 x  5)  5 x  13
2.) 2x  9  3x  9  5x
4.)  7  x  19
6.) 6( x  2)  2(2 x  4)
Wetzel
Math 101
2.3 – Problem Solving
Application Problems:
WORD PROBLEMS!!
To Solve:
1.) Understand the problem. Organizing the given information by sketching a
diagram, making a table, or just rewriting it and know exactly what the problem is asking
you to find.
2.) Derive a plan to solve the problem. This may not even require any writing.
3.) Carry your plan out. Solve the problem!
4.) Completely answer the question making sure your answer makes sense!.
There may be more than one answer or an answer may not make sense so you would
cancel it out. Include any units in the answer.
I. Geometry Problems:
The third side of an isosceles triangle is 2 inches shorter than each of the other
two sides. If the perimeter of this triangle is 67 inches, find the length of each side.
II. Consecutive Integer Problems:
The sum of three consecutive integers is 186. Find the three integers.
III. Motion Problems:
D=R*T
Angela made the 300 mile drive to Las Vegas in 6 hours. What was her rate for
the trip?
EXTRA PRACTICE:
1.) The sum of four consecutive even integers is 508. Find the integers.
2.) One number is 5 more than twice another number. If the sum of the two numbers is
80, find the two numbers.
3.) Lance heads directly east at a constant rate of 25 miles per hour. One hour later, Levi
leaves the same spot heading directly west at a constant rate of 20 miles per hour. How
long after Levi leaves will the two cyclists be 250 miles apart?
4.) A homeowner has a rectangular garden in her backyard. The length of the garden is 9
times as long as the width, and the perimeter is 160 feet. Find the dimensions of the
garden.
Wetzel
Math 101
2.4 – Percents, Ratios, & Proportions
What is a percent?
Complete the table.
Percent
Decimal
Fraction
25 1

100 4
25%
.25
36%
______
______
_____
.045
______
_____
______
7
10
What is a ratio?
What is a proportion?
To Solve: Cross-Multiply
1.) Multiply one numerator by the opposite denominator.
2.) Set that equal to the other numerator multiplied by the other denominator.
3.) Solve the remaining equation.
Ex.:
1.)
3 21

8 x
2.)
x2 3

12
4
Applications:
I. Is over Of Method:
is
%

of 100
Ex.:
3.) What percent of 80 is 24?
4.) What is 600% of 53?
5.) The average score for a class on test 1 was 88. The average score for test 2 was 77.
What was the percent decrease in the average score from test 1 to test 2?
II. Mixture Problems:
A bartender has rum that is 40% alcohol. How much rum and how much cola
need to be mixed together to make 5 liters of rum and cola that is 16% alcohol?
III. Interest Problems:
I  Pr t
Diane was given $35,000 when she retired. She invested some at 7% interest and
the rest at 9% interest. If she earned $2910 in interest in one year, how much was
invested in each account?
EXTRA PRACTICE.
1.) You divided an inheritance of $6000 between two investments
earning 4% and 10% simple interest. During one year the two accounts
earned $500. How much did you invest in each account?
2.) A chemist needs to mix together a 10% alcohol solution with a 30%
alcohol solution to form 100 gallons of a 25% alcohol solution. How
much of each solution must he mix together?
3.) A 12oz. bag of potato chips has 50% free written across the top of it. What was the
original size of the bag?
Wetzel
Math 101
2.5 – Linear Inequalities
Inequality Symbols:
<
>
Graphing on a number line:
less than
greater than
 less than or equal to
 greater than or equal to
1.) Number line with significant numbers
2.) Open or Closed circle
3.) Arrow to the left or right
Interval Notation:
1.) Beginning Value, Ending Value
2.)  and - 
3.) ( ) or [ ]
Linear Inequality: (One Variable)
To Solve:
1.) Solve as if it were an equation with one additional rule,
**2.) If you mult. or divide by a negative, “flip” the inequality sign
Compound Inequalities ( “And” Inequalites)
*Solve for the variable in the middle
“Or” Inequalities
*Solve both inequalites. Solutions will be in one or the other.
Examples: Solve in Interval Notation and Graph.
1.) 2 x  5( x  3)  x  9
2.) 7( x  4)  21
3.)  8  3x  7  28
4.) x  4  7 or x  8  1