Transcript Ch.2.notes_x - Windsor C

Algebra I
Chapter 2
Section 2-1 Writing Equations
Ex1) Translate each sentence into an equation.
Pay attention to the words is, is as much as, is
the same as, is identical to
a) Seven times a numbers squared is five times
the difference of k and m
a) Fifteen times a number subtracted from 80 is
25
Section 2-1
Ex2) Translate the sentence into a formula: the
area of a triangle equals the product of ½ the
length of the base and the height
Ex3) Translate each equation into a sentence
a) 6z – 15 = 45
b) y2 + 3x = w
Section 2-2: Solving One-Step
Equations
Solution –
Equivalent Equations –
Property Name
Addition Prop. Of Equality
Subtraction Prop. Of Equality
Multiplication Prop. Of Equality
Division Prop. Of Equality
Symbols
Example
Section 2-2: Solving One-Step
Equations
Solution – the value(s) that make an equation true
Equivalent Equations – equations that have the same
solution
Property Name
Addition Prop. Of Equality
Subtraction Prop. Of Equality
Multiplication Prop. Of Equality
Division Prop. Of Equality
Symbols
Example
Section 2-2
Ex1) Solve the one-step equations and check
your answer!
a) x – 22 = 54
b) y + 63 = 79
c) 3m = -12
e)
2
x =8
3
d)
a
=5
7
f) 5 = -6 + n
Section 2-2
Ex2) Of a group of female students surveyed,
225 or about 9 said they talk on the phone
20
while they
watch t.v. How many girls were
surveyed?
Section 2-2
Ex3) Solve
a) g + 5 = 33
c)
r 1
=
5 2
b) 104 = y – 67
d)
2
n = 10
7
Section 2-3 Solving Multi-Step
Equations
Ex1) Solve
a) 11x – 4 = 29
b)
c) 2a – 6 = 4
d)
a+7
=5
8
n +1
= 15
-2
Section 2-3
Ex2) Sarah is buying a pair of water skis that are
on sale for 2/3 of the original price. After he
uses a $25 gift certificate, the total cost before
taxes is $115. What was the original price of the
skis? Write an equation and solve.
Section 2-3
Consecutive Integers – integers in counting
order
Type
Words
Consecutive Integers
Integers in counting
order
Consecutive Even
Integers
Even integers in
counting order
Consecutive Odd
Integers
Odd integers in
counting order
Symbols
Example
Section 2-3
Ex3) Write an equation for the following
problem, then solve the equation. Find 3
consecutive odd integers with a sum of -51
Section 2-4: Solving Equations with
Variables on Both Sides
Steps for Solving Equations with Multiple Steps
1.
2.
3.
4.
5.
Section 2-4: Solving Equations with
Variables on Both Sides
Steps for Solving Equations with Multiple Steps
1. Distribute (get rid of parenthesis)
2. Combine Like terms on the same side of =
3. Get variables together on one side of =
4. Add or subtract the number NOT attached to the
variable
5. Multiply or divide the number that IS attached to
the variable
Section 2-4
Ex1) Solve
a) 2 + 5k = 3k – 6
b) 3w + 2 = 7w
c) 5a + 2 = 6 – 7a
d) 2x +1 = -32 x - 6
Section 2-4: Equations with Grouping
Symbols
Ex2)
a) 6(5m - 3) = 1 (24m +12) b) 8s – 10 = 3(6 – 2s)
3
c) 7(n – 1) = -2(3 + n)
Section 2-4: Special Solutions
Ex2) Solve
a) 5x + 5 = 3(5x – 4) – 10x
b) 3(2b – 1) – 7 = 6b – 10
Section 2-4
Find the value of x so that the
figures have the same area
Find the value of x so that
the figures have the same
perimeter
10cm
x
x cm
6
6 cm
x
3cm x cm
2x + 2
Section 2-5: Solving Equations
Involving Absolute Value
Absolute Value – The distance a point is from
zero on a number line
Ex1) Evaluate
a) m + 6 -14 if m = 4
b) 23- 3- 4x if x = 2
Section 2-5
Solve the absolute value
equation
Ex2) f + 5 =17
Steps
1. Split the equation into
2 equations, one that
= the positive number
and one that = the
negative number
2. Solve each equation
(you will have 2
answers!)
Section 2-5
Ex3) Solve
a)
b -1 = -3 b)
4t -8 = 20
c)
3
a-3 = 9
4
Ex4) Write an absolute value equation for the graph
with points on 11 and 19 (draw a graph)
Section 2-6: Ratios and Proportions
Ratio –
Proportion –
Means-Extremes Property of Proportion
Words
Symbols
Examples
Section 2-6: Ratios and Proportions
Ratio – A comparison between two numbers
using division (fraction)
Proportion – two ratios that are equal
Means-Extremes
Property
of of
Proportion
Words
In a proportion,
the product
the extremes is equal to
the product of the means
Symbols
If , a = c and b and d do not equal zero, then ad = bc
b
Examples
Since
d
2 1
, 2(2) = 4(1) or 4 = 4
=
4 2
Section 2-6
Ex1) Determine if the ratios are equivalent.
Answer yes or no.
a) 3 , 18
b) 29.2 , 7.3
c) 8.4 = 8.8
7 42
10.4 2.6
9.2
9.6
Section 2-6
Ex2) Use cross-multiplication to solve the
proportions
a) x = 3
b) x - 2 = 2
c) 7 = 21
10
5
14
7
x+9
36
Section 2-6
Ex3) The Ramsey Cascades Trail is about 1 1
8
inches long on a map with a scale of
3 in = 10 miles. What is the actual length of the
trail. Let l represent the length.
Section 2-7 Percent of Change
Percent of Change –
Percent of Increase –
Percent of Decrease –
Section 2-7 Percent of Change
Percent of Change – the ratio of the change in
an amount to the original amount expressed as
a percent
Percent of Increase – when the new number is
greater than the original number
Percent of Decrease – when the new number is
less than the original number
Section 2-7
Ex1) Determine whether each percent of change
is a percent increase or a percent decrease.
Then find the percent of change.
a) Original: 20
b) Original: 25
Final: 23
Final: 17
Section 2-7
Ex2) The total number of passengers on cruise
ships increased 10% from 2007 to 2009, how
many were there in 2007?
Section 2-7
Ex3) Marta is purchasing wire and beads to make
jewelry. Her merchandise is $28.62 before tax. If the
tax is 7.25% of the total sales, what is the final cost?
Ex4) Since Tyrell has earned good grades in school,
he qualifies for the good student discount on his car
insurance. His monthly payment without the
discount is $85. If the discount is 20%, what will he
pay each month?