Algebra Unit 2

Solve the following equations.

x + 0 = 5 1x = 6

x = 5 x = 6Are numbers allowed to disappear? Yes Only which two numbers can disappear? 0 and 1

is the same as is the same as

Tuesday Oct 13, 2020 Activator

Page #3 Lesson 2.1

Today’s Objective Unit 2Lesson 1

Students will be able to solve one step equations.

Solve the one step equation.

y + 7 = -4 What is happening to the variable?

What is the identity for subtraction? 0

Add 7

Subtract 7

Solve means to get the variable by itself.

-7 -7y + 0 = -11

y = -11

Today’s New Vocab (1 of 4)

Solve means do opposites

https://www.youtube.com/watch?v=NybHckSEQBI 3:30

Today’s New Vocab (2 of 4)Solve the one step equation.

w - 5 = 8 What is happening to the variable?

Solve means do opposites

Add 5

Subtract 5

What is the identity for addition? 0

+5 +5w + 0 = 13

w = 13

Today’s New Vocab (3 of 4)Solve the one step equation.

-80 = 4h What is happening to the variable?

What is the identity for division? 1

Multiply 4

Divide 4

÷ 4 ÷ 4-20 = 1h-20 = h

Solve means do opposites

Today’s New Vocab (4 of 4)Solve the one step equation.

-15 = 𝑘

−5

What is happening to the variable?

Multiply -5

Divide -5

What is the identity for multiplication? 1

(-5) (-5)+75 = 1k+75 = k

Solve means do opposites

.

Solve for x.𝑥

2= 8

Same answer or different answers? Different Why?

(2) (2)

1x = 16 x = 16

What number disappears? 1

Why? We multiplied

or divided.

2x = 8÷ 2 ÷ 2

1x = 4x = 4

Tuesday Oct 13, 2020 WP Page #2 Lesson 2.1

Solve 𝑥

−2= -4 Solve – 2 + x = -10

Same answer or different answers? Different

(-2) (-2) +2 +2

1x = 8

x = 8

0 + x = -8

x = -8

Tuesday Oct 13, 2020 Exit Ticket

.

y - 5 = -11 -5 + y = -11

Same answer or different answers? Same Why?

Solve for y.What number disappears? 0

Why? identity of

addition

+5 +5 y+0 = -6

Y = -6

+5 +5 0 + y = -6

y = -6

Thursday Oct 15, 2020 Activator Page #7 Lesson 2.2

Today’s Objective

Students will be able to solve two step equations.

Lesson 2.2

Solve 𝑥

2= -4 Solve 2x = -4

(2) (2) 1x = -8

x = -8

Today’s New Vocab (1 of 4)

÷ 2 ÷ 2

1x = −2x = −2

Equal sign in the question, always equal sign in the answer.

Solve means to do the opposite.

Today’s New Vocab (2 of 4)Solve the two step equation.

-5x + 4 = -6 What is happening to x? Multiplied by -5Then, add 4

Do the opposite backwards

Subtract 4Divide by -5

-5x = -10

x = 2÷−5 ÷ −5

-4 -4

Today’s New Vocab (3 of 4)Solve the two-step equation. 𝑥

−3- 5 = 7

What is happening to x? Divided by -3Then, subtract 5

Do the opposite backwards

Add 5multiply by -3

𝑥

−3= 12

x = -36

+5 +5

(-3) (-3)

Today’s New Vocab (4 of 4)Solve the two step equation. -12 =

3𝐴

−4 What is happening to x? Multiplied by 3Then, Divided by -4

Do the opposite backwards

Multiply by -4Divide by 3

(-4) (-4)

+48 = 3A

16 = A

÷ 3 ÷ 3

Thursday Oct 15, 2020

.

2x - 6 + 1 = 19

Can anything be done to only one side of the equation? YES Why?

2x - 5 = 19

One side is called an expression.

Distribute

Combine Like Terms

Page #8 Lesson 2.2

Thursday Oct 15, 2020 Exit Ticket

.2x - 5 = 19Solve for x.

2x - 5 = 19+5 +52x = 24

x = 12

÷ 2 ÷ 2

2(12) - 5 = 1924 - 5 = 19

19 = 19Yes, the last equation is TRUE.

SubstitutionCheck your work. How?

Doesx = 12?

Monday Oct 19, 2020 Activator Solve the left equation.

3x + 4x = 21 4x = 3x + 7

The x’s are on different sides of the equation =.

7x = 21

x = 3

1x = 0 + 7x = 7

-3x -3x

÷ 7 ÷ 7

Why can’t the x’s be added on the right equation?

Page #11 Lesson 2.3

Today’s Objective

Students will be able to solve equations with variables on both sides.

Lesson 2.3

Today’s New Vocab (1 of 4)Write an equation.

Two times a number added to twelve is the same as

Negative five times a number subtracted by nine

Let x = an unknown

number 2x + 12 = -5x - 9

Today’s New Vocab (2 of 4)

How do you get variables to the same side? Add or Subtract

2x + 12 = -5x - 9 2x + 12 = -5x - 9 -2x -2x +5x +5x

12 = -7x - 9 7x + 12 = - 9 If you were to solve both equations, would you get the same answer?

Do the first step of the equation.

Yes Why?

Today’s New Vocab (3 of 4)Finish solving.

What’s happening?(7) and + 12

Do the oppositebackwards.

-12 and ÷ 7

7x + 12 = - 9

7x = - 21

x = - 3

-12 -12

÷ 7 ÷ 7

Today’s New Vocab (4 of 4)Is x = -3 a solution to this equation? Yes

Because, the last equation is true.

Substitute

Distribute

Combine Like Terms

2x + 12 = -5x - 9 2(-3) + 12 = -5(-3) - 9

-6 + 12 = 15 - 9 6 = 6

Monday Oct 19, 2020 Work Period

.10x – 35 = 15x - 10-10x - 10x

– 35 = 5x - 10+10 + 10– 25 = 5x ÷ 5 ÷ 5−5 = 𝑥

Solve thisequation.

Page # 12Lesson 2.3

Monday Oct 19, 2020 Exit Ticket

.

This candy store sells one pound bags of candy. If the one pound price is $8, what is the cost per ounce, x? Write and solve an equation.

Cost per ounce is $0.50

How many ounces are in a pound? 16$8 = 16x

$0.50 = x

÷ 16 ÷ 16

Total Cost ounces times cost

Let x = cost per ounce

Wednesday Oct 21, 2020 Activator Solve the equation and inequality.

2x – 7 > 1 2x – 7 = 1

What’s happening?(2) and - 7

Do the opposite.+7 and ÷ 2

Did you solve the problem in a similar way? Yes

+7 +7 +7 +72x = 8

x = 4

2x > 8 ÷ 2 ÷ 2 ÷ 2 ÷ 2

x > 4

Page #15 Lesson 2.4

Today’s Objective

Students will be able to solve and graph inequalities in one variable.

Lesson 2.4

.

Write an inequality for the graphs. 𝑥 ≥ −2

𝑥 > −2 𝑥 < −2

𝑥 ≤ −2

Today’s New Vocab (1 of 4)https://www.youtube.com/watch?v=W87ymSALLiM 0:30-2:30

Today’s New Vocab (2 of 4)Solve and graph the inequality.

-9x ≥ 18 ÷ -9 ÷ -9

x ≤ −2

Flip the inequality

when you multiply or divide by a negative

Today’s New Vocab (3 of 4)Solve and graph the inequality.

𝑥

−3< 2

(−3) (−3)x > −6

Flip the inequality when you multiply or divide by a negative

Today’s New Vocab (4 of 4)

x + 2 < -3Graph the inequality.

Open circle Closed circle

Shade LeftShade Right

x < -5-2 -2

Did we flip the inequality? No

Graph the inequality.

Wednesday Oct 21, 2020 WP

.

Solve and Graphthe inequality.

3x – 5 < -2x + 15+2x +2x 5x – 5 < +15

+5 +5 5x < 20

x < 4÷5 ÷5

https://www.youtube.com/watch?v=SHD6sSBePZ4 0-2:30

Saving on fuel can help…(1) A person’s budget(2) The environment

Page #16Lesson 2.4

.-5x - 4 = -14Solve the equation.

-5x - 4 > -14+4 +4

-5x = -10

x = 2

÷−5 ÷ −5

Wednesday Oct 21, 2020 Exit Ticket

+4 +4-5x > -10

x < 2÷−5 ÷ −5

Remember to FLIP the inequality when you multiply or divide by a negative

Solve the inequality.

Tuesday Oct 27, 2020 Activator

𝑥

−3+ 9 < -6

Solve the inequality.

Explain the answer in words.

𝑥

−3< -15

X > 45

-9 -9

(-3) (-3) Is 10 a solution? No, 10 is not > 45.

Page #19Lesson 2.5

Flip the inequality when you multiply or divide by a negative

Today’s Objective

Students will be able to substitute and solve word problem equations.

Lesson 2.5

Today’s New Vocab (1 of 4)Write the inequality. Then, Substitute.

Let x = an unknown number

Y ≥ 2x + 300 To use a variable

https://www.youtube.com/watch?v=3fYD_3V6MWUVideo: Y=MX+B Real-Life Equations 2:20

Sarah is paid $300 per week and $2 per eye liner that she sells. If she sells 350 eye liners, can she pay her $1000 in bills? YES

Y = 𝑚x + b

Y ≥ 2(350) + 300 Y ≥ 700 + 300

Today’s New Vocab (2 of 4)

Tony is 2 more than triple Andrea’s age. Tony is 6 less than four times Andrea’s age. How old is Andrea?

Write the two equations.

Let T = Tony’s age Let A = Andrea’s age

Let StatementT = 2 + 3A

and T = 4A – 6

Today’s New Vocab (3 of 4)T = 2 + 3A T = 4A – 6

Solve the two equations.

2 + 3A = 4A – 6

2 = 1A – 6

8 = 1A What’s happening?

(1) and -6 Do the opposite.

+6 and ÷ 1

-3A -3A

+6 + 6

÷ 1 ÷ 18 = A

If two things are equal to the same thing, then they are equal.

Today’s New Vocab (4 of 4)

T = 2 + 3A T = 4A – 6 How old is Tony? If Andrea is 8.

T = 2 + 3(8) T = 4(8) - 6

T = 2 + 24T = 26

T = 32 - 6T = 26

Tony is 26 years old.

Tuesday Oct 27, 2020 Work Period

.

Songs can be purchased on iTunes for $0.99. Sandy

figured she would be charged $49.50 for 50 songs.

Is she correct? Let s = the number of songs downloaded.

Let p = the total price

p = $0.99s p = $0.99(50) p = $49.50

Yes, she is correct.

Page #20Lesson 2.5

Tuesday Oct 27, 2020 Exit Ticket

.

A Sprint charges $40.00 a month for up to 1 gigabyte of data.

The cost of additional data is $0.02 per megabyte.

d = the number of additional megabytes used and

C = the total charges at the end of the month,

Write the linear equation for user's monthly bill.

What would be the cost of 1000 megabytes (1GB) extra?

C = $0.02d + $40C = $0.02(1000) + $40C = $20 + $40

C = $60

Thursday Oct 29, 2020 Activator Solve the both equations for x.

x – 8 = -24 x – y = -z

Do you solve the problems the same way? Yes

x = -24 + 8 x = -16

+8 +8x = -z + y x = -z + y

+y +y

Can –z+y be combined ? No Why? Not like terms

Page #23Lesson 2.6

Today’s Objective

Students will be able to solve literal equations.

Lesson 2.6

Today’s New Vocab (1 of 4)Solve for x in terms of C.

6x = 12C What’s happening to x? (6)

Do the opposite to x. ÷ 6

÷ 6 ÷ 6

x = 2c

Can other variables be in the answer? YES https://www.youtube.com/watch?v=-Y9y3T0GO7E

Video 2:45 seconds.

Today’s New Vocab (2 of 4)Solve for x in terms of B and C.

6x – 18B = 12C+ 18B + 18B

6x = 12C + 18B

What’s happening to x?(6) and -18B

Do the opposite to x.+18B and ÷ 6÷ 6 ÷ 6

x = 2C + 3B

Today’s New Vocab (3 of 4)

Solve for x interms of D and R.

𝐷 =𝑥 − 𝑅

2

What’s happening to x?−𝑅 and ÷ 2

Do the opposite to x.(2) and +𝑅

(2) (2)

2𝐷 = 𝑥 − 𝑅

+𝑅 +𝑅

2D+R = x

https://www.youtube.com/watch?v=ZQQ7wrEzUr8 14:53-16:20

Today’s New Vocab (4 of 4)Rx – C = 6 Solve for x in

terms of R and C. What’s happening to x?(𝑅) and −𝐶

Do the opposite to x.+C and ÷ 𝑅

+ C + CRx = 6 + C

÷ 𝑅 ÷ 𝑅

x = 6+𝐶

𝑅

Thursday Oct 29, 2020 Work Period

.

Evaluate (substitute)and solve for x in terms

of A = 2 and B = 6.

𝐴𝑋

𝐵= 5

2𝑋

6= 5

2x = 30

x = 15

(6) (6)

÷ 2 ÷ 2Page #24Lesson 2.6

Thursday Oct 29, 2020 Exit Ticket

.

Solve for x interms of A and B.

𝐴𝑋

𝐵= 5

(B) (B) AX = 5𝐵

X = 5𝐵

𝐴

÷ 𝐴 ÷ 𝐴

What’s happening to x?(𝐴) and ÷ 𝐵

Do the opposite to x.(B) and ÷ 𝐴

Thursday Nov 5, 2020 Activator

#7

The last equation is TRUE (correct/yes).

Today’s Objective

Students will be able to review all objectives from Unit #2.

Today’s New Vocab (1 of 4)#10

Today’s New Vocab (2 of 4)

#12

Today’s New Vocab (3 of 4)

#13

.

Today’s New Vocab (4 of 4)

Open circle Closed circle

Shade LeftShade Right

Did we flip the inequality? No

Graph the inequality.

x ≤ 4

#14

Thursday Nov 5, 2020 Exit ticket Make the inequalities true when x = -2.

X < 0 X > -100

There are lots of correct answers on this question.

(-2) < 0 (-2) > -100

Yes, True Yes, True

Monday Nov 9, 2020 Test #2Test 2 requirements #1: Send Mr. V all of your Classwork 2.1-2.6#2: Did you do your Boom Cards for Unit 2?#3: Do Test 2: Submit answers with Google Forms.

Test #2 can be found here (after scrolling down). https://mrvanscoyk.weebly.com/algebra.html