Transcript Chapter 7

Chapter 7
Pre Algebra
Solving Two-Step Equations
Two-Step
Equations
1/19
Two operations are required to
isolate x
Plug and Chug to check your answer
Solving
Two Step
Equations
Ask five questions about
the inequality:
1. What is the variable?
2. What is the first operation
being done to the variable?
3. What is the inverse operation?
4. What is the second operation
being done to the variable?
5. What is the inverse operation?
Work
First—undo any addition or
Backwards subtraction
Second—undo any
multiplication or division
Example
1. x
2. • -2
3.  -2
-2x – 5 = 25
+5 +5
-2x = 30
-2
-2
Draw “the road”
Work Backwards
Add 5 to both sides
Simplify
Divide both sides by -2
Simplify
x = -15
4. -5
5. +5
-2(-15) – 5 = 25
30 – 5 = 25
25 = 25
Check your answer
Plug and Chug
You Try
Solve
1. y – 4 = -12
2
2. –4m + 10 = 30
3. ¼a – 13 = -3
You Try
Workbook
p 113
Solving Multi-Step Equations
Multi-Step
Equations
1/20
Simplify (use the distributive
property to get rid of parenthesis)
Combine like terms
Follow steps to solve a two step
equation.
Simplify
-3( a + 6)
4(3m – 7)
-8(5r – 2)
Combine
like terms
3d + 4 -12d + 7
5(9n – 4) -15 + 7n
6k + 3 – 2(k – 1)
Solve
8a + 4a = 144
3(n - 2) = 36
-3(2y + 7) = -18
Consecutive Counting by ones---integers
(positive and negative whole
Integers
numbers) that come right after
each other.
1, 2, 3
-11, -10, -9
Represented algebraically as
n, n+1, n+2
Example
The sum of two consecutive
integers is 131
n + (n+1) = 131
The sum of four consecutive
integers is -22
n + (n+1) + (n+2) + (n+3) = -22
You Try
Workbook
p 116
Writing Equations
Homework
problems
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1. The sale price of a sweater is $48. the
price is 20% less than the original
price. What was the original price?
2. Elena has $240 in the bank, She
withdraws $15 cash each week to pay
for piano lessons. How many lessons
can she afford with her savings?
3. The perimeter of a rectangle is 64 cm.
The length is 4 cm less than twice the
width. Find the length and width.
4. Wendy bought a drill at a 10% off
sale. The sale price was $75.60.
Find the original price p.
5. Lamar’s summer job is mowing lawns
for a landscaper. His pay is $7.50/h.
Lamar also makes $11.25/h for any
time over 40 hours he works in one
week. He worked 40 h last week
plus n overtime hours and made
$339.38. Home many over time
hours did he work?
6. Find two whole numbers with a sum
of 15 and a product of 54.
7. A farmer is building a square pen 21
ft on each side. He puts one post at
each corer and one post every 3 feet
between. How many posts will he
use?
8. It takes 8 painters 6 hours to paint the
walls of a gym.
a. How many person hours does the job
require?
b. How many hours will 12 painter take
to paint the gym?
9. Cathy has a collection of dimes and
quarters. The number of dimes
equals the number of quarters. She
has a total of $2.80. How many of
each coin does Cathy have?
10. The weight of an object on Venus is about
9/10 of its weight on Earth. The weight of an
object an Jupiter is above 13/5 times the
weight on Earth.
a. If a rock weights 23ib on Venus, how much
would it weight on Earth?
b. If the same rock was on Jupiter, how much
would it weigh?
11. Jackson, Petra, and Tyrone went to the
beach and collected sea shells over the
weekend. Jackson collected s sea shells and
Petra and Tyrone each collected 13 fewer that
than twice the number of sea shells Jackson
collected. At the end of the weekend, they
has 94 seashells. How many seashells did
each person collect?
Chapter 7 Practice Test
2/1
Show all steps. Show all work
1. The sale price of a coat is $24. the
price is 40% less than the original
price. What was the original price?
2. 2x + 4 = 12
3. 3(2x -5) = 14
4. 5x - 3 + 2x + 5 = 16
5. -¼ (16x + 32) +2x = 34
6. 3x + 17 = 5x - 13
Chapter 7 Quiz
2/3
Show all steps. Show all work
1. The sale price of a coat is $31. the
price is 70% less than the original
price. What was the original price?
2. 3x + 5 = -20
3. 7(3x -5) = 7
4. 9x - 8 + 7x + 6 = 2
5. -5x + 10 = 2x - 11
Transforming Formulas
Transforming
Formulas
2/8
Manipulating an equation to solve for a
specific variable
Use the properties of equality to
transform the equations (p 86, 88, 92,
93 in your book)
Examples
Solve the area formula A = lw for w
Solve x = y – z for z
Solve the distance formula d = rt for rate
Solve the perimeter formula p = 2l + 2w
for w
Solve A = ½ h(a + b) for a
Simple and Compound Interest 2/10
Principal
The original amount of money
deposited into or borrowed from an
account
Simple
Interest
When interest is only calculated on
the principal.
Formula
I = prt
Interest = principal x rate x time(years)
Example Find the simple interest after 5
years on a savings account with
an initial deposit of $325 and a
rate of 2%
I = prt
I is what we are looking for
p is $325
r is 2%
t is 5 years
Compound When interest is only calculated on
Interest
balance.
Balance Principal plus interest
Formula
B = p(1 + r)n
Balance = principal x ( 1 + rate) raised
to the number of interest periods