algebra unit 2
TRANSCRIPT
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