Transcript x - Nutley Schools

Chapter 3 Review Day 2
Algebraic Equations
Multiplication with Subtraction
2x – 4 = 8
+4 +4
2x = 12
2
2
x = 6
Algebraic Equations
Multiplication with Addition
5x + 10 = 80
-10 -10
5x = 70
5
5
x = 14
Algebraic Equations
Multiplication with Subtraction
-3x – 4 = -82
+4 +4
-3x = -78
-3
-3
x = 26
Algebraic Equations
Multiplication with Addition
2/3x + 2 = 8
-2 -2
(HINT)
Reciprocal
3
2
2
3
x = 6
3
2
x = 18/2 = 9
Algebraic Equations
Division with Addition
x/5 + 2 = 8
-2 -2
x
(5)
5
= 6 (5)
x = 30
Algebraic Equations
C.L.T.
(4x +6x )+ 20 = 80
10x + 20 = 80
-20 -20
10x = 60
10
10
x=6
Algebraic Equations
C.L.T.
(3x + 2x) +(20 - 8)= 92
5x + 12 = 92
-12 -12
5x = 80
5
5
x = 16
Algebraic Equations
C.L.T.
6x + 15 = 125 + 4x
(6x – 4x) + 12 = 122 +(4x – 4x)
2x + 12 = 122
-12 -12
2x = 110
2
2
X = 55
Algebraic Equations
Distributive Property
2(5x – 6) – 3x = 4(x + 12) – 9x
10x – 12 - 3x = 4x + 48 – 9x
(10x – 3x)-12 =(4x – 9x)+ 48
7x - 12
= -5x + 48
(7x + 5x)- 12 = 48
12x - 12 = 48
Algebraic Equations
Distributive Property
7x + 5x - 12 = 48
12x - 12 = 48
+12 +12
12x
= 60
12
12
X=5
Lesson 3.3, For use with pages 148-153
1. Simplify the expression 9x + 2(x – 1) + 7.
ANSWER
11x + 5
Solve the equation.
2. 5g – 7 = 58
ANSWER
13
Lesson 3.3, For use with pages 148-153
Solve the equation.
3. 2 x = 18
3
ANSWER
27
4. A surf shop charges $85 for surfing lessons and $35 per
hour to rent a surfboard. Anna paid $225. Find the
number of hours she spent surfing.
ANSWER
4h
Daily Homework Quiz
Solve the equation.
1.
a
+ 6 = –14
4
ANSWER
2.
–80
6r – 12 = 6
ANSWER
3. – 36 = 7y + 2y
ANSWER
3
–4
For use after Lesson 3.2
Daily Homework Quiz
For use after Lesson 3.2
4. The output of a function is 9 less than 3 times the input.
Write an equation for the function and then find the
input when the output is –6.
ANSWER
y = 3x – 9; 1
5. A bank charges $5.00 per month plus $.30 per check for
a standard checking account. Find the number of checks
Justine wrote if she paid $8.30 in fees last month.
ANSWER
11 checks
EXAMPLE 1
Solve an equation by combining like terms
Solve 8x – 3x – 10 = 20.
8x – 3x – 10 = 20
Write original equation.
5x – 10 = 20
Combine like terms.
5x – 10 + 10 = 20 + 10
Add 10 to each side.
5x = 30
Simplify.
5x = 30
5
5
Divide each side by 5.
x=6
Simplify.
EXAMPLE 2 Solve an equation using the distributive property
Solve 7x + 2(x + 6) = 39.
SOLUTION
When solving an equation, you may feel comfortable doing
some steps mentally. Method 2 shows a solution where some
steps are done mentally.
EXAMPLE 2
METHOD 1
Show All Steps
METHOD 2
Do Some Steps Mentally
7x + 2(x + 6) = 39
7x + 2(x + 6) = 39
7x + 2x + 12 = 39
7x + 2x + 12 = 39
9x + 12 = 39
9x + 12 = 39
9x + 12 – 12 = 39 – 12
9x = 27
9x 27
=
9
9
x= 3
9x = 27
x=3
EXAMPLE 3
Standardized Test Practice
SOLUTION
In Step 2, the distributive property is used to simplify the left
side of the equation. Because –4(x – 3) = –4x + 12,
Step 2 should be 5x – 4x + 12 = 17.
ANSWER
The correct answer is D.
A B
C
D
GUIDED PRACTICE
for Examples 1, 2, and 3
Solve the equation. Check your solution.
1.
9d – 2d + 4 = 32
ANSWER
4
EXAMPLE
2
GUIDED PRACTICE
for Examples 1, 2, and 3
Solve the equation. Check your solution.
2.
2w + 3(w + 4) = 27
ANSWER 3
EXAMPLE
2
GUIDED PRACTICE
for Examples 1, 2, and 3
Solve the equation. Check your solution.
3.
6x – 2(x – 5) = 46
ANSWER 9
EXAMPLE 4
Solve
2
3
Multiply by a reciprocal to solve an equation
3 (3x + 5) = –24.
2
3 (3x + 5) = –24
2
3 (3x + 5) = 2 (–24)
2
3
3x + 5 = –16
3x = –21
x = –7
Write original equation.
Multiply each side by
reciprocal of 3.
2
,2the
3
Simplify.
Subtract 5 from each side.
Divide each side by 3.
EXAMPLE
4 Multiply by
foraExample
4 to solve an equation
reciprocal
GUIDED PRACTICE
Solve the equation. Check your solution.
3 (z – 6) = 12
4.
4
ANSWER 22
EXAMPLE
4 Multiply by
foraExample
4 to solve an equation
reciprocal
GUIDED PRACTICE
Solve the equation. Check your solution.
5.
2 (3r + 4) = 10
5
ANSWER
7
EXAMPLE
4 Multiply by
foraExample
4 to solve an equation
reciprocal
GUIDED PRACTICE
Solve the equation. Check your solution.
6.
– 4 (4a – 1) = 28
5
ANSWER –8.5
There are actually three different
possible outcomes when solving for a
variable.
1. One solution
2. No Solutions
3. Infinitely Many
Solutions
Let’s try some examples…
Solve the following for the indicated variable:
4x  10  2x  6
x = -8
5 y  2 y 1  3 y  2
No
Solution
20  x  19  2x
X=
1
3
 2  4r  7  5  4r
Infinitely
Many
Solutions
Your Turn…
Solve the following for the indicated variable:
4x  8
 10
2
x = -7
3n
8
 13
12
n = 20
3(a  1)  5  3a  2
Infinitely many Solutions
5
3
t t  3 t
2
2
No Solutions
Warm up
Solve the following for the indicated variable:
1. 3x  8  14
2.
2  4x  18
x
 5  8
3.
3
x
4. 2(  15)  48
2
Warm up Answers
1.
2.
3.
4.
x  2
x 5
x  9
x  18
So, to change a percentage into a
decimal, you always divide by
100
For example, 35% as a fraction is 35/100 so to
change this into a decimal, you divide 35 by
100
35%
÷ 100
0.35
To change decimal into a
percentage
Decimal
Percentage
To change a decimal into a
percentage, you X by 100
0.23 X 100
23%
Problem 1
Brittany Berrier became a famous
skater. She won 85% of her
meets. If she had 250 meets in
2000, how many did she win?
212.5 meets
Problem 2
Krystyl Ferguson worked
at the zoo. If 3 of her
17 baboons were sick,
What % were sick?
About 18%
Problem 3
Matt Debord worked as a
produce manager for Walmart.
If 35 people bought green
peppers and this was 28% of
the
total customers, how many
customers did he have?
125
Problem 4
Emily Lower was a great
WNBA ball player. They
made $700,000 a year. If
they owed 22% for taxes,
how much did they pay in
taxes? $154,000 in taxes
Problem 5
Tiffany Lowery got 65 referrals
during the year. If 14% of
these were for tardies,
how many times did she get
caught for being tardy?
9.1 tardies
Problem 6
Brett Mull became a famous D.J.
He played a total of 185 C.D’s in
January. If he played 35 classical
C.D.’s, what is the percent of classica
C.D.’s he played.
About 19%
Problem 7
Brett Smith became a doctor.
He fixed elephant trunks. He
fixed 78.5% of all the elephants he
treated. He fixed 45 elephant
trunks. How many elephants did
he treat in all.
About 57.32 trunks
Problem 8
Ashley Scalf became a famous
golfer. She did occasionally hit
one into the pond. If she hit 7 out
of 85 hits into the pond, what
percentage did she hit into the pond.
About 8.2%
Problem 9
Jeremy Devereaux got the
nice guy award. If 42
people voted and Jeremy
got 85% of the votes, how
many people voted for
Jeremy?About 35.7 people
Problem 10
Brad (the Bull) Denton and
Daniel (Killer) McFalls
joined the WWE. They won 16
of their 23 bouts. What
percentage did they win.
About 69.6%
Problem 11
Sarah Roderick and Erin
Lanning became Las Vegas
show girls. If they paid $45,000
in taxes and they made
$3,000,000 per year, what
percentage did they pay in
taxes? 1.5%
EXAMPLE
5 Write andfor
Example
5
solve
an equation
GUIDED PRACTICE
7.
WHAT IF? Suppose the cranes take 12 days (288 hours) to
travel the 2500 miles. How many hours of this migration are
the cranes not flying?
ANSWER
188 h