Chapter 3 Review Day 2

Algebraic EquationsMultiplication with Subtraction

2x – 4 = 8+4+4

2x = 122 2x = 6

Algebraic EquationsMultiplication with Addition

5x + 10 = 80-10-10

5x = 705 5x = 14

Algebraic EquationsMultiplication with Subtraction

-3x – 4 = -82+4+4

-3x = -78-3 -3x = 26

Algebraic EquationsMultiplication with Addition

2/3x + 2 = 8-2-2

x = 6

x = 18/2 = 9

23(HINT)

Reciprocal

32

32

Algebraic EquationsDivision with Addition

x/5 + 2 = 8-2-2

= 6

x = 30

x5

(5) (5)

Algebraic Equations

C.L.T.

-20-20

10x = 6010

4x +6x + 20 = 80( )10x + 20 = 80

10

x = 6

Algebraic Equations

C.L.T.

-12-12

5x = 805

3x + 2x + 20 - 8 = 92

5x + 12 = 92

5

x = 16

( ) ( )

Algebraic Equations

C.L.T.

-12-122x + 12 =122

2

6x + 15 = 125 + 4x

6x – 4x + 12 = 122 + 4x – 4x

22x = 110

( ) ( )

X = 55

( )

10x – 3x -12 = 4x – 9x + 48

Algebraic Equations

Distributive Property

7x - 12 = -5x + 48

2(5x – 6) – 3x = 4(x + 12) – 9x

10x – 12 - 3x = 4x + 48 – 9x

( )

7x + 5x - 12 = 48

12x - 12 = 48

( )

12 12

7x + 5x - 12 = 48 12x - 12 = 48

+12+12

12x = 60

X = 5

Algebraic Equations

Distributive Property

Lesson 3.3, For use with pages 148-153

1. Simplify the expression 9x + 2(x – 1) + 7.

ANSWER 11x + 5

2. 5g – 7 = 58

ANSWER 13

Solve the equation.

Lesson 3.3, For use with pages 148-153

ANSWER

ANSWER 4 h

Solve the equation.

x 3. 23

= 18

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.

Daily Homework Quiz For use after Lesson 3.2

Solve the equation.

1. + 6 = –14 a 4

ANSWER 80–

2. 6r – 12 = 6

ANSWER 3

3. 36 = 7y 2y+–

ANSWER 4–

Daily Homework Quiz For use after Lesson 3.2

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.

4.

ANSWER y = 3x 9; 1–

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.

5.

ANSWER 11 checks

Solve an equation by combining like termsEXAMPLE 1

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.

Divide each side by 5.

x = 6 Simplify.

= 305

5x5

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 1Show All Steps

7x + 2(x + 6) = 39

7x + 2x + 12 = 39

9x + 12 = 39

9x + 12 – 12 = 39 – 12

9x = 27

x = 3=

9x9

279

METHOD 2Do Some Steps Mentally

7x + 2(x + 6) = 39

7x + 2x + 12 = 39

9x + 12 = 39

9x = 27

x = 3

Standardized Test PracticeEXAMPLE 3

ANSWER

The correct answer is D. A C DB

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.

GUIDED PRACTICE for Examples 1, 2, and 3

9d – 2d + 4 = 321.

Solve the equation. Check your solution.

4ANSWER

EXAMPLE 2GUIDED PRACTICE for Examples 1, 2, and 3

2w + 3(w + 4) = 272.

3ANSWER

Solve the equation. Check your solution.

EXAMPLE 2GUIDED PRACTICE for Examples 1, 2, and 3

6x – 2(x – 5) = 463.

9ANSWER

Solve the equation. Check your solution.

Multiply by a reciprocal to solve an equation

EXAMPLE 4

Write original equation.32

(3x + 5) = –24

23

32

(3x + 5) = (–24)23

Multiply each side by , the reciprocal of .

233

2

3x + 5 = –16 Simplify.

3x = –21 Subtract 5 from each side.

x = –7 Divide each side by 3.

32

(3x + 5) = –24Solve .

Multiply by a reciprocal to solve an equation

EXAMPLE 4GUIDED PRACTICE for Example 4

34

(z – 6) = 124.

Solve the equation. Check your solution.

22ANSWER

Multiply by a reciprocal to solve an equation

EXAMPLE 4GUIDED PRACTICE for Example 4

25

(3r + 4) = 105.

Solve the equation. Check your solution.

7ANSWER

Multiply by a reciprocal to solve an equationEXAMPLE 4GUIDED PRACTICE for Example 4

6. 45

(4a – 1) = 28–

Solve the equation. Check your solution.

–8.5ANSWER

There are actually three different possible outcomes when solving for a variable.

1. One solution

2. No Solutions2. No Solutions

3. Infinitely Many 3. Infinitely Many SolutionsSolutions

Let’s try some examples…

Solve the following for the indicated variable:

x = -8

62104 xx xx 21920

5 2 1 3 2y y y

No Solution

rr 45742

Infinitely Many Solutions

X = 1

3

Your Turn…Solve the following for the indicated variable:

n = 20

Infinitely many Solutionsx = -7

No Solutions

102

84

x

1312

38

n

235)1(3 aa

ttt2

33

2

5

Warm up

Solve the following for the indicated variable:

1.

2.

3.

4.

3 8 14x

5 83

x

2 4 18x

2( 15) 482

x

Warm up Answers1.

2.

3.

4.

2x

18x 9x

5x

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% 0.35÷ 100

To change decimal into a percentage

Decimal

PercentageTo change a decimal into a

percentage, you X by 100

0.23 23%X 100

Problem 1

Brittany Berrier became a famousskater. She won 85% of her meets. If she had 250 meets in2000, how many did she win?

212.5 meets

Problem 2

Krystyl Ferguson workedat the zoo. If 3 of her17 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 manycustomers did he have?

125

Problem 4Emily 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 referralsduring the year. If 14% of these were for tardies,how many times did she getcaught for being tardy?

9.1 tardies

Problem 6

Brett Mull became a famous D.J.He played a total of 185 C.D’s inJanuary. If he played 35 classicalC.D.’s, what is the percent of classicalC.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 hetreated. He fixed 45 elephanttrunks. How many elephants didhe treat in all.

About 57.32 trunks

Problem 8

Ashley Scalf became a famousgolfer. She did occasionally hitone into the pond. If she hit 7 outof 85 hits into the pond, what percentage did she hit into the pond.

About 8.2%

Problem 9

Jeremy Devereaux got thenice guy award. If 42people voted and Jeremygot 85% of the votes, howmany people voted for Jeremy?About 35.7 people

Problem 10

Brad (the Bull) Denton and Daniel (Killer) McFallsjoined the WWE. They won 16 of their 23 bouts. What percentage did they win.

About 69.6%

Problem 11

Sarah Roderick and ErinLanning became Las Vegasshow girls. If they paid $45,000in taxes and they made $3,000,000 per year, what percentage did they pay in taxes? 1.5%

EXAMPLE 5 Write and solve an equationGUIDED PRACTICE for Example 5

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?

188 hANSWER