Solving Equations with Variables on Both Sides of the Equal Sign
Notes Page 5: Solving Equations with Variables on Both Sides of the Equal Sign
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Solving Inequalities
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Main Idea: Representing Relations and Functions
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Vertical Line Test
Page 7-What are Functions?
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Equations as Functions--Graphing by Functions
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Evaluating Expressions and Functions
Notes Page 3 Equations as Functions
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Day 3 Wednesday (12/10/25)
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Arithmetic Sequences
Page 8-Arithmetic Sequences
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Finding Slope
Notes Page 9 Rate of Change and Slope
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Slope Formula
Notes Page 10 Slope Formula
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Day 4: Thursday (12/11/25)
Graphing Slope-Intercept Form
Notes Graphing Linear Equations--Using Slope-Intercept Form
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Graphing Using x and y Intercepts
Notes Page Graphing Using x and y Intercepts
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Graphing Using Point-Slope Form
Notes Page 11--Point Slope Form
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Linear Word Problems
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Mathematical Phrases into Expressions
Question 1
1.
Translate this expression.
“eighteen less than a number”
Question 2
2.
Translate this expression.
“the product of a number and six”
Question 3
3.
Translate this expression.
“triple a number”
Question 4
4.
Translate this expression.
“a number increased by nine”
Question 5
5.
Translate this expression.
“the quotient of a twenty and a number”
Question 6
6.
Write each expression in words
-12+n
Question 7
7.
Write each expression in words
-2/n
Question 8
8.
Write each expression in words
9x
Question 9
9.
Write each expression in words
3k-14
Question 10
10.
1. How many terms does the expression have?
_______
2. What are the variables?
_______ and _______
3. What are the coefficients?
_______ and _______
4. What is the constant?
_______
Question 11
11.
1. How many terms does the expression have?
_______
2. What are the variables?
_______ and _______ and _______
3. What are the coefficients?
_______ and _______ and _______
4. What is the constant?
_______
Question 12
12.
Directions: Simplify each expression.
Question 13
13.
Directions: Simplify each expression.
Question 14
14.
Directions: Give the perimeter of each figure as a simplified expression.
Question 15
15.
Simplify each expression by distributing.
Question 16
16.
Simplify each expression by distributing and combining like terms.
Question 17
17.
Simplify each expression by distributing and combining like terms.
Question 18
18.
Evaluate each expression using the variable replacements.
Question 19
19.
The cost of either a can of gourmet chili is $2.25 and a can of hearty soup is $1.75. Ton Nam bought cans of chili and soup. He wrote an expression to describe the purchase where c represents the number of cans of chili and s represents the number of cans of soup.
Write an expression to present how much he might spend based on the number of cans of each that he bought.
_______
How much will it cost to buy 6 cans of chili and 7 cans of soup?
_______
Solving Equations
Question 20
20.
Draggable item
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Corresponding Item
arrow_right_alt
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arrow_right_alt
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Question 21
21.
Question 22
22.
Question 23
23.
Question 24
24.
Solve this equation:
Question 25
25.
Question 26
26.
Question 27
27.
Solve this equation:
17 + 3k = 26
Question 28
28.
Solve this equation:
15h - 9 = - 54
Question 29
29.
Solve this equation:
Question 30
30.
Solve this equation:
Solving Multi-Step Equations
Question 31
31.
Question 32
32.
Solve this multi-step equation. Show your work (SYW)
Question 33
33.
Question 34
34.
Solve this multi-step equation. Show your work (SYW)
Question 35
35.
Solve this multi-step equation. Show your work (SYW)
Question 36
36.
Solve this equation
Question 37
37.
Solve this equation
Solving Proportions
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Question 38
38.
Cross multiply and fill in each box with the right product.
a. _______
b. _______
Question 39
39.
Solve each proportion. Show your work!
Question 40
40.
Solve each proportion. Show your work!
Question 41
41.
Solve each proportion. Show your work!
Question 42
42.
Jasmine bought 1000 robux for $8 with her parents' money. At the same exchange rate, how many robux can Lisa buy if she stole $24 from her parents?
Question 43
43.
Solve and graph the inequality for the given variable.
Question 44
44.
Solve and graph the inequality for the given variable.
Question 45
45.
Solve and graph the inequality for the given variable.
Question 46
46.
Use the set of ordered pairs to complete the relation table, relation mapping, and coordinate graph.
Relations vs. Functions
Page 7-What are Functions?
Question 47
47.
Determine whether the given relation is a function. (Function or Not a Function)
Question 48
48.
Determine whether the given relation is a function. (Function or Not a Function)
Question 49
49.
Determine whether the given relation is a function. (Function or Not a Function)
Question 50
50.
Determine whether the given relation is a function. (Function or Not a Function)
Question 51
51.
Determine whether the given relation is a function. (Function or Not a Function)
Question 52
52.
Determine whether the given relation is a function. (Function or Not a Function)
Question 53
53.
Determine whether the given relation is a function. (Function or Not a Function)
Question 54
54.
Directions: Complete each function table, then graph the function.
Question 55
55.
Evaluate each function for the given value.
Question 56
56.
Evaluate each function for the given value.
Question 57
57.
Evaluate each function for the given value.
Arithmetic Sequences
Page 8-Arithmetic Sequences
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Question 58
58.
Find the next three terms of each sequence.
3, 7, 11, 15, _______ ,_______ ,_______
Question 59
59.
Find the next three terms of each sequence.
10, 6, 2, _______ ,_______ ,_______
Question 60
60.
What does f(1) mean?
Question 61
61.
What does f(n) mean?
Question 62
62.
What does d mean?
Question 63
63.
What does n mean?
Question 64
64.
What is the explicit rule of this arithmetic sequence?
Question 65
65.
What is the explicit rule of this arithmetic sequence?
Question 66
66.
Find the first term and common difference in this sequence:
1, 3, 5, 7, ...
a₁=_______
d=_______
Write the explicit formula to find the nᵗʰ term of this sequence (you can use either notation):_______
Find the 70ᵗʰ term of this sequence:
_______
Question 67
67.
Find the first term and common difference in this sequence:
-1, -4, -7, -10, ...
a₁=_______
d=_______
Write an equation to find the nᵗʰ term of this sequence (you can use either notation):_______
Find the 24ᵗʰ term of this sequence:_______
Question 68
68.
Charlie deposited $300 in a savings account. Each week thereafter, he deposits $35 into the account.
Write a formula to represent this sequence._______
How much total money has Charlie
deposited after 30 weeks?
_______
How many weeks would it take to save at up at least $2000
_______
Question 69
69.
Find the slope of this line:
Question 70
70.
Find the slope of this line:
Slope-Intercept Form
Notes Slope-Intercept Form
Slope-Intercept Form
Slope (m)
y-intercept (b)
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Question 71
71.
Question 72
72.
Write the equation in slope intercept form with the given information:
Question 73
73.
Write the equation in slope intercept form with the given information:
Question 74
74.
Write the equation of this line in slope-intercept form.
Question 75
75.
Write the equation of this line in slope-intercept form.
Question 76
76.
Directions: Find the slope between each pair of points:
(1, 9) and (3, 9)
Question 77
77.
Directions: Find the slope between each pair of points:
(-5, 8) and (-7, 5)
Question 78
78.
Directions: Find the slope between each pair of points:
(-4, 8) and (-4, 5)
Question 79
79.
Use the slope and the y-intercept of each equation to graph the equation.
y=mx+b
y=-2x-2
slope:
_______
y-intercept:
_______
Question 80
80.
Use the slope and the y-intercept of each equation to graph the equation.
y=mx+b
slope:
_______
y-intercept:
_______
Question 81
81.
Write the equation of of the line represented on the graph.
slope:
_______
y-intercept:
_______
Equation of the line:
_______
Question 82
82.
What are the x and y-intercepts of this function?
x-intercept
_______
y-intercept
_______
Question 83
83.
Use x and y-intercepts of this equation to graph it.
Question 84
84.
Use x and y-intercepts of this equation to graph it.
Question 85
85.
Write the equation of the line that passes through the given two points. Write all final answers in slope-intercept form.
Slope-_______
Slope-intercept Form-_______
Question 86
86.
Write the equation of the line that passes through the given two points. Write all final answers in slope-intercept form.
Slope-_______
Slope-intercept Form-_______
Question 87
87.
Write the equation of the line that passes through the given two points. Write all final answers in slope-intercept form.
Slope-_______
Slope-intercept Form-_______
Question 88
88.
A city parking garage charges a flat rate of $10.00 for parking 2 hours or less, and $0.50 per hour for each additional hour.
Write a linear model that gives the total charge if you parked more than 2 hours._______
How much does it cost to park a car in the parking gargage for 7 hours?
_______
Question 89
89.
Sarah is saving money to buy a e-bike that costs $900. She already has $120 saved, and she plans to save an additional $30 each week from her job working at Del Taco.
Write a linear equation that shows how much money she is saving._______
How much money will she have saved in 2 months?_______
How many weeks will it take Sarah to save enough money to buy the bicycle?
_______
Question 90
90.
The cost for 7 dance lessons is $82. The cost for 11 lessons is $122.
Write an equation that can calculate the cost of dance lessons. (Use point-slope form)
_______
Find the cost of 4 lessons.
_______
Question 91
91.
A climber is on a hike. After 2 hours he is at an altitude of 400 feet. After 6 hours, he is at an altitude of 700 feet.
How many feet can he climb in 1 hour? (Find the slope)
_______
Write an equation that can calculate the how many feet a climber can climb in a given amount of hours. (Use point-slope form).
_______
How many feet can this person climb in 12 hours of climbing?
_______
Match the operation with its inverse.
inverse of subtraction
subtraction
inverse of division
addition
inverse of addition
division
inverse of multiplication
multiplication
Put these operations in the order by which you perform them to simplify an expression. (first to last)
parentheses ( )
addition
multiplication
exponents
division
subtraction
To solve an equation we need to undo operations to isolate a variable.So, we need toundoPEMDAS. This means we need to work in a different order.
Put these operations in the order by which you perform them to solve an equation. (first to last)
Combine like terms
Undo division and multiplication
Undo subtraction and addition
parentheses ( )
Put the steps to solving this equation in the right order.
divide both sides of the equation by 3
add 7 to both sides of the equation
the result is a=7
Before we start solving, we identify the variable a, so we can solve for it the variable
What is the first step to solving this equation?
subtracting both sides of the equation by 11
multiplying both sides of the equation by 4
subtraction both sides of the equation by 3
dividing both sides of the equation by 4
What is the second step to solving this equation?
multiplying both sides of the equation by 4
subtracting both sides of the equation by 11
subtraction both sides of the equation by 3
dividing both sides of the equation by 4
Put the steps in the correct order to solve this multistep equation.
undo subtract 20 by adding 20 to both sides of the equations to get -28a = -140
Check the solution by evaluating the original expression -4(7a+5) to verify that it equals -160
Use distribution to multiply (7a+5) by -4 to get -28a - 20
undo multiplying by -28 by dividing by both sides of the equation by -28 to get a = 5
The solution is a = 5
Put the steps in the correct order to solve this multistep equation.
undo subtract 3 by adding 3 to both sides of the equations to get -7x = 28
undo multiplying by -7 by dividing by both sides of the equation by -7 to get x = -4
Simplify like terms to get the equation -7x - 3 = 25
The solution is x = -4
Check the solution by evaluating the original expression -4x -7 - 3x +4 to verify that it equals 25
Given the slope and y-intercept of the line, write the equation