Equation Power Slides EQUATION CODEBREAKERS
Mission: Solving for the Unknown
The Mission
Objective
Use inverse operations to isolate the variable and find the secret value.
Vocabulary
• Variable: A letter representing a number.
• Equation: A math sentence stating two parts are equal.
The Inverse Pairs
-
Addition & Subtraction
They undo each other.
×
÷
Multiplication & Division
The perfect partners.
Case Study: Addition
\(x + 10 = 13\)
Step 1: Identify Operation
Addition (+10)
Step 2: Inverse Action
Subtract (-10)
"Whatever you do to one side, you must do to the other!"
Case Study: Multiplication
\(6w = 60\)
Step 1: Identify Operation
Multiplication (times 6)
Step 2: Inverse Action
Division (divide by 6)
\(w = 10\)
Is \(x = 4\) the Solution?
Check each equation by substituting the value. If it works, it's a "True Solution".
A) \(x + 3 = 7\)
B) \(x - 4 = 0\)
C) \(1 + x = 4\)
D) \(x \cdot 2 = 8\)
Warning: Only 3 of these are correct. Which one is the imposter?
Basic Codebreaker Worksheet Level 1: Foundational Training
BASIC CODEBREAKER
AGENT NAME:
DATE:
Training Mission
Find the secret value of the letter (the variable). Use the opposite operation to solve!
1
Guided Training Case
\(x + 3 = 10\)
What is happening? Addition (+3)
Opposite action: Subtract (-3) from both sides.
\(x = 7\)
Check: \(7 + 3 = 10\)
2
Active Cases
\(x + 2 = 8\)
Hint: The operation is addition. Use subtraction to undo it!
Work Space
\(x = \_\_\_\_\_\)
\(w - 5 = 10\)
Hint: The operation is subtraction. Use addition to undo it!
Work Space
\(w = \_\_\_\_\_\)
\(2y = 10\)
Hint: \(2y\) means 2 times y. Use division to undo it!
Work Space
\(y = \_\_\_\_\_\)
Self-Correction Zone
Once you find your answer, put it back into the equation. Does it make sense? (Example: If \(x=6\), does \(6+2=8\)? Yes!)
Master Codebreaker Worksheet Level 2: Target Mastery
Master Codebreaker
Investigator:
Case Date:
1
Field Operations
Solve each equation using inverse operations. You must show all steps to receive full credit for the case.
A) \(x + 23 = 61\)
VALUE:
B) \(k - 15 = 47\)
VALUE:
C) \(12m = 108\)
VALUE:
D) \(\frac{y}{4} = 13\)
VALUE:
2
Witness Statements
"I had a certain number of secret files (\(f\)) on my desk. My partner brought me 14 more. Now, I have a total of 39 files."
Equation Representation:
Number of original files (\(f\)):
3
Intelligence Analysis
Identify all equations where \(n = 8\) is the correct solution. (Mark with an 'X')
\(n - 3 = 5\)
\(n + 8 = 16\)
\(4n = 32\)
\(12 - n = 5\)
Elite Codebreaker Worksheet Level 3: Elite Extension
Elite Codebreaker
Special Agent:
Secure Date:
1
Precision Intel
Elite agents deal with complex data. Solve these equations involving decimals and fractions. Show your precise steps.
\(x - 4.75 = 12.3\)
INVERSE OPERATION:
Calculations Area
\(x = \_\_\_\_\_\_\)
\(\frac{2}{3}y = 10\)
INVERSE OPERATION:
Calculations Area
\(y = \_\_\_\_\_\_\)
2
The Supply Drop
An elite team received a shipment of medical supplies. The total weight of the shipment was 45.5 kg. If there were 7 identical kits in the shipment, how much did each kit (\(k\)) weigh?
Define the Equation:
Solve for \(k\):
3
System Verification
Which of the following phrases is equivalent to the equation \(3(x + 2) = 18\)?
Three times the sum of a number and two is eighteen.
Two more than three times a number is eighteen.
The product of three and a number plus two is eighteen.
Codebreaker Solution Key INVESTIGATOR KEY
Equation Codebreakers • Answer Guide
Basic Codebreaker (Level 1)
Part 1: Guided Training
\(x + 3 = 10 \Rightarrow x = 7\)
Operation: Addition. Inverse: Subtraction.
Part 2: Active Cases
Case A: \(x + 2 = 8\)
Case B: \(w - 5 = 10\)
Case C: \(2y = 10\)
Master Codebreaker (Level 2)
Part 1: Field Operations
A) \(x = 38\)
B) \(k = 62\)
C) \(m = 9\)
D) \(y = 52\)
Part 2: Witness Statements
Equation: \(f + 14 = 39\)
Solution: 25 files
Part 3: Intelligence
Correct equations for \(n = 8\):
\(n - 3 = 5\) (True: \(8-3=5\))
\(4n = 32\) (True: \(4 \cdot 8 = 32\))
Elite Codebreaker (Level 3)
Part 1: Precision Intel
\(x = 17.05\) (Add 4.75)
\(y = 15\) (Multiply by 3/2)
Part 2: Supply Drop
Equation: \(7k = 45.5\)
Solution: 6.5 kg per kit
Part 3: System Verification
"Three times the sum of a number and two is eighteen."
Confidential Answer Guide • For Educator Eyes Only
Codebreaker Mastery Test Official Certification
CODEBREAKER MASTERY TEST
Agent:
Clearance Date:
SECTION 1
Target Verification
1. Select all the equations where \(x = 5\) is the correct solution.
Helper Hint: Replace the letter with 5. Does the math work out?
\(x + 5 = 10\)
\(x - 5 = 0\)
\(10 + x = 12\)
\(2x = 10\)
\(x \cdot 3 = 15\)
\(x + 10 = 50\)
SECTION 2
Active Codebreaking
2. Solve the equation for \(x\):
Hint: Use subtraction to undo addition!
\(x + 10 = 25\)
\(x =\)
3. Solve the equation for \(w\):
Hint: Divide by 4 to undo multiplication!
\(4w = 20\)
A) 4
B) 5
C) 16
D) 24
4. Solve for \(y\):
Hint: Multiply by 2 to undo division!
\(\frac{y}{2} = 8\)
\(y =\)
SECTION 3
Scenario Modeling
5. Detective Sarah had 10 evidence bags . After a busy day at the crime scene, she has a total of 25 bags .
(a) Which equation helps find the number of new bags, \(b\), Sarah collected?
\(25b = 10\)
\(10 + b = 25\)
\(25 + 10 = b\)
\(b - 10 = 25\)
(b) How many new bags were collected?
Total New Bags:
SECTION 4
Verbal Translation
6. Which algebraic expression represents "five more than the product of two and \(n\)"?
A) \(2n + 5\)
B) \(5n + 2\)
C) \(n + 7\)
D) \(2n - 5\)
End of Assessment • Security Code: ONE-STEP-EASY-2026
Mastery Test Answer Key ANSWER KEY
Codebreaker Mastery Test (Simplified) • Professional Use Only
Section 1: Target Verification
1. Equations where \(x = 5\) is the correct solution:
\(x + 5 = 10\) (True: \(5 + 5 = 10\))
\(x - 5 = 0\) (True: \(5 - 5 = 0\))
\(2x = 10\) (True: \(2 \cdot 5 = 10\))
\(x \cdot 3 = 15\) (True: \(5 \cdot 3 = 15\))
Incorrect options: \(10 + x = 12\) (results in 15), \(x + 10 = 50\) (results in 15).
Section 2: Active Codebreaking
2. \(x + 10 = 25\):
\(x = 15\)
Operation: Subtraction (\(25 - 10\))
3. \(4w = 20\):
B) 5
Operation: Division (\(20 \div 4\))
4. \(\frac{y}{2} = 8\):
\(y = 16\)
Operation: Multiplication (\(8 \times 2\))
Section 3: Scenario Modeling
5 (a) Equation Choice:
\(10 + b = 25\)
5 (b) Number of New Bags:
15 bags
Working: Sarah started with 10, total is 25. \(25 - 10 = 15\).
Section 4: Verbal Translation
6. "Five more than the product of two and \(n\)":
A) \(2n + 5\)
Explanation: "Product" means multiplication (\(2n\)). "Five more" means adding 5.
End of Answer Key • Mastery Guide
