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W21 - Friday

Total questions: 79

Worksheet time: 40mins

Name
Class
Date
1.
Welcome to today's lesson on identifying solutions to a two‐step linear inequality in one variable! Let's begin by recalling what a two‐step inequality is.
a)
Continue
b)
Stop
2.

Fill in the blank: An expression that compares two values using symbols like <, >, ≤, or ≥ is called an (a)   .

3.
What is a two‐step inequality?
a)
An inequality solved using one operation
b)
An inequality solved using two operations
c)
An inequality solved using three operations
d)
Not an inequality
e)
Inequality with no solution
4.
Which ancient civilization is known for early developments in algebra?
a)
Egyptians
b)
Babylonians
c)
Greeks
d)
Romans
e)
Chinese
5.
What is the first step when solving a two‐step inequality like 8y + 9 ≥ -23?
a)
Add the constant
b)
Subtract the constant
c)
Multiply both sides by 2
d)
Divide both sides by the variable
e)
None of these
6.
After subtracting 9 from both sides, what inequality do we get from 8y + 9 ≥ -23?
a)
8y ≥ -32
b)
8y ≥ -14
c)
8y ≥ -23
d)
8y ≥ 14
e)
8y ≥ 23
7.
Which operation is used to isolate y after subtracting the constant in 8y + 9 ≥ -23?
a)
Addition
b)
Subtraction
c)
Multiplication
d)
Division
e)
Exponentiation
8.
Divide both sides of 8y ≥ -32 by 8. What is the result?
a)
y ≥ -4
b)
y ≥ 4
c)
y ≥ -32
d)
y ≥ 8
e)
y ≥ 0
9.
Is the value y = -4 a solution to 8y + 9 ≥ -23?
a)
Yes
b)
No
c)
Maybe
d)
Not enough information
e)
None of these
10.

Fill in the blank: The final answer to 8y + 9 ≥ -23 is y ≥ (a)   .

11.
In which of the following real-world measurements are inequalities commonly used? (Select all that apply)
a)
Temperature
b)
Time
c)
Distance
d)
Pressure
e)
Age
12.
Who is known as the "Father of Algebra"?
a)
Pythagoras
b)
Euclid
c)
Al-Khwarizmi
d)
Archimedes
e)
Fibonacci
13.
The symbol for "greater than or equal to" is _______.
a)
≥
b)
≤
c)
>
d)
<
e)
equal
14.

True or False: If you multiply or divide both sides of an inequality by a negative number, the inequality sign must be reversed.

(a)  

15.
Which two steps are commonly used to solve a two‐step inequality?
a)
Combine like terms and factor
b)
Subtract the constant and divide by the coefficient
c)
Multiply by the coefficient and add the constant
d)
Divide by the variable and add the constant
e)
None of the above
16.
Which operation is NOT typically used in solving two‐step inequalities?
a)
Subtraction
b)
Division
c)
Addition
d)
Exponentiation
e)
Multiplication
17.
If we mistakenly added 9 instead of subtracting in 8y + 9 ≥ -23, what incorrect result would we get?
a)
8y ≥ -14
b)
8y ≥ -32
c)
8y ≥ -23
d)
8y ≥ 32
e)
8y ≥ 14
18.

Fill in the blank: The process of performing the same operation on both sides of an inequality to keep it balanced is called (a)   .

19.
What is the first step in checking if a number is a solution to an inequality?
a)
Substitute the number into the inequality
b)
Multiply the number
c)
Divide the number
d)
Ignore the constant
e)
Rearrange the inequality
20.
What operations do we typically perform to isolate the variable in a two‐step inequality?
a)
Addition then subtraction
b)
Subtraction then division
c)
Multiplication then addition
d)
Division then subtraction
e)
Subtraction then multiplication
21.
Example 1: Start with the inequality 8y + 9 ≥ -23. What is our first step?
a)
Subtract 9 from both sides to isolate the term with y
b)
Add 9 to both sides
c)
Multiply both sides by 8
d)
Divide both sides by 9
e)
Ignore the constant
22.

(8y + 9 ≥ -23.) After subtracting 9 , what inequality do we obtain?

a)
8y ≥ -32
b)
8y ≥ -14
c)
8y ≥ -23
d)
8y ≥ 14
e)
8y ≥ 23
23.
Step 2: Dividing both sides of 8y ≥ -32 by 8 illustrates which property?
a)
Multiplicative Identity
b)
Division Property of Inequality
c)
Addition Property of Equality
d)
Zero Product Property
e)
Subtraction Property
24.

(8y ≥ -32) What is the result after dividing both sides by 8?

a)
y ≥ -4
b)
y ≥ 4
c)
y ≥ -32
d)
y ≥ 8
e)
y ≥ 0
25.
Step 3: To verify, substitute y = 0 into the original inequality. Does it satisfy 8(0) + 9 ≥ -23?
a)
Yes
b)
No
c)
Maybe
d)
Not enough information
e)
None of these
26.
Now, test y = -5. Does it satisfy 8(-5) + 9 ≥ -23?
a)
Yes
b)
No
c)
Maybe
d)
Not enough information
e)
Cannot determine
27.
Step 4: Summarize the solution set for 8y + 9 ≥ -23.
a)
y < -4
b)
y > -4
c)
y ≥ -4
d)
y ≤ -4
e)
y = -4
28.
Example 2: For the inequality 17 > -4u + 5, what is the first operation to isolate u?
a)
Subtract 5 from both sides
b)
Add 5 to both sides
c)
Multiply both sides by -4
d)
Divide both sides by -4
e)
Subtract u from both sides
29.

(17 > -4u + 5) After subtracting 5, what is the new inequality?

a)
12 > -4u
b)
22 > -4u
c)
17 > -4u
d)
12 < -4u
e)
22 < -4u
30.
When dividing both sides of 12 > -4u by -4, what critical step must be taken?
a)
Keep the inequality sign unchanged
b)
Reverse the inequality sign
c)
Multiply by -1 after division
d)
Add 4 to both sides
e)
Subtract 4 from both sides
31.

(12 > -4u) After dividing by -4 and reversing the sign, what is the solution for u?

a)
u > -3
b)
u < -3
c)
u = -3
d)
u ≥ -3
e)
u ≤ -3
32.
Verify the solution for u by testing u = 0. Does it satisfy 17 > -4(0) + 5?
a)
Yes
b)
No
c)
Maybe
d)
Not enough information
e)
None
33.

Test u = -10. Does it satisfy the inequality 17 > -4(-10) + 5?

a)
Yes
b)
No
c)
Maybe
d)
Not enough information
e)
None
34.

Fill in the blank: The process of reversing the inequality sign when dividing by a negative number is called (a)   .

35.
Step 4: Conclude the solution for 17 > -4u + 5.
a)
u < -3
b)
u > -3
c)
u = -3
d)
u ≥ -3
e)
u ≤ -3
36.
Why is it important to flip the inequality sign when dividing by a negative number?
a)
To preserve the truth of the inequality
b)
To reverse the order of the numbers
c)
Because negative numbers are smaller
d)
Both 1 and 2
e)
None of these
37.

Fill in the blank: The method of solving inequalities by performing inverse operations to isolate the variable is called (a)   .

38.
Review: What are the two main operations used to solve a two‐step inequality?
a)
Addition and subtraction
b)
Subtraction and division
c)
Multiplication and division
d)
Addition and multiplication
e)
Subtraction and multiplication
39.
Quiz: Solve the inequality 5x - 3 < 12. First, add 3 to both sides. What is the resulting inequality?
a)
5x < 15
b)
5x < 9
c)
5x < 12
d)
5x < 3
e)
5x < -15
40.
After obtaining 5x < 15, divide by 5. What is the final solution for x?
a)
x < 3
b)
x < -3
c)
x < 15
d)
x > 3
e)
x = 3
41.
Which of the following are true about operations on inequalities? (Select all that apply)
a)
You can add the same number to both sides
b)
You can multiply by a positive number without changing the inequality
c)
Dividing by a negative number reverses the inequality sign
d)
Subtracting the same number from both sides preserves the inequality
e)
Multiplying by zero always reverses the inequality
42.
In the inequality -2y + 4 ≥ 10, what is the first step to isolate y?
a)
Subtract 4 from both sides
b)
Add 2y to both sides
c)
Divide by -2
d)
Multiply by -2
e)
None of these
43.
After subtracting 4 from -2y + 4 ≥ 10, what is the new inequality?
a)
-2y ≥ 6
b)
2y ≥ 6
c)
-2y ≥ 14
d)
2y ≥ 14
e)
-2y ≥ 10
44.
When dividing -2y ≥ 6 by -2, what must you do with the inequality sign?
a)
Keep it the same
b)
Reverse it
c)
Remove it
d)
Double it
e)
Square it
45.
What is the final solution to -2y + 4 ≥ 10?
a)
y ≥ -3
b)
y ≤ -3
c)
y = -3
d)
y > -3
e)
y < -3
46.
Which historical mathematician is credited with significant contributions to algebra?
a)
Euclid
b)
Al-Khwarizmi
c)
Pythagoras
d)
Newton
e)
Gauss
47.

Fill in the blank: The symbol '<' is used to denote (a)   .

48.
Why do we reverse the inequality sign when multiplying or dividing by a negative number?
a)
To preserve the truth of the inequality
b)
Because negative numbers reverse order
c)
To make calculations easier
d)
All of the above
e)
None of these
49.

Today we'll learn about identifying solutions to a two‐step linear inequality in one variable. Are you ready to begin?

a)
Yes, I'm ready!
b)
No
50.

Fill in the blank: An expression that shows the relationship between two values using <, >, ≤, or ≥ is called an (a)   .

51.
What is a two‐step inequality?
a)
An inequality solved in one step
b)
An inequality solved in two steps
c)
An inequality with no operations
d)
An equation
52.
Historical note: Which mathematician is known as the "Father of Algebra"?
a)
Pythagoras
b)
Euclid
c)
Al-Khwarizmi
d)
Archimedes
53.
What is the first step when solving the inequality (w/3) - 16 ≤ 11?
a)
Multiply both sides by 3
b)
Add 16 to both sides
c)
Subtract 16 from both sides
d)
Divide both sides by 3
54.

Fill in the blank: When you perform the same operation on both sides of an inequality, you are (a)   the inequality.

55.

Fill in the blank: The symbol "≤" means "less than or (a)   ."

56.

True or False: Solving inequalities is similar to solving equations, except you must reverse the inequality sign when multiplying or dividing by a negative number.

(a)  

57.
Checkbox: In which of the following are negative numbers particularly relevant?
a)
Temperature
b)
Grades
c)
Height
d)
Elevation
e)
Age
58.
Let's begin our step-by-step example. We need to solve (w/3) - 16 ≤ 11 for w. Which operation should we perform first?
a)
Multiply both sides by 3
b)
Add 16 to both sides
c)
Subtract 16 from both sides
d)
Divide both sides by 3
59.
When we add 16 to both sides of (w/3) - 16 ≤ 11, what is the arithmetic expression on the right-hand side?
a)
11 + 16
b)
11 - 16
c)
w + 16
d)
w - 16
60.

Fill in the blank: Adding 16 to both sides of an inequality is an example of the (a)   property.

61.

(w/3) - 16 ≤ 11) After adding 16, the inequality becomes (w/3) ≤ (a)   .

62.
What is the next step to solve (w/3) ≤ 27?
a)
Subtract 3 from both sides
b)
Multiply both sides by 3
c)
Divide both sides by 27
d)
Add 3 to both sides
63.
When you multiply both sides of (w/3) ≤ 27 by 3, what expression do you obtain for w?
a)
w = 27
b)
w = 81
c)
w ≤ 81
d)
w/3 = 81
64.

Fill in the blank: The final answer to (w/3) - 16 ≤ 11 is w ≤ (a)   .

65.
Now that we have solved the inequality, is the same process used when solving equations?
a)
Yes, except when dealing with negatives
b)
No, it's entirely different
c)
Yes, it's exactly the same
d)
No, because inequalities have no unique solution
66.

Type "Proceed" to continue.

(a)  

67.

Fill in the blank: Multiplying both sides by 3 demonstrates the (a)   property.

68.
What is the final solution set for the inequality (w/3) - 16 ≤ 11?
a)
w = 81
b)
w > 81
c)
w ≤ 81
d)
w < 81
69.
Why do we perform the same operation on both sides of an inequality?
a)
To keep the inequality balanced
b)
To change the inequality sign
c)
To confuse the variable
d)
To simplify calculations only
70.
Interdisciplinary: Which scientific field frequently uses inequalities to describe ranges of measurements?
a)
Biology
b)
Chemistry
c)
Physics
d)
All of the above
71.
Historical connection: Which ancient civilization is known for early algebraic methods, including solving inequalities?
a)
Romans
b)
Babylonians
c)
Vikings
d)
Egyptians
72.

Fill in the blank: The symbol "/" in (w/3) represents (a)   .

73.
After obtaining w/3 ≤ 27, what arithmetic operation isolates w?
a)
Division
b)
Multiplication
c)
Addition
d)
Subtraction
74.
When multiplying both sides of w/3 ≤ 27 by 3, which property are we using?
a)
Commutative Property
b)
Associative Property
c)
Multiplicative Property
d)
Distributive Property
75.
What lesson do we learn from the consistency of operations used in both equations and inequalities?
a)
They are completely different
b)
They share many properties but differ with negatives
c)
They are identical in every way
d)
They are random processes
76.

Fill in the blank: Solving inequalities requires applying inverse operations in a (a)   manner.

77.
True or False: When solving inequalities, you must reverse the inequality sign when multiplying by a positive number.
a)
True
b)
False
78.
Quiz: True or False: The solution to a two‐step inequality represents a range of values, not a single value.
a)
True
b)
False
79.

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