Understanding Solving Equations in Grade 2 - Mathematics - Exercises with solutions

Master equation solving: unknowns, balancing operations, and basic algebraic thinking through these 10 detailed exercises.

Solutions: Exercises 1 to 10
1 Basic Addition Equations
Exercise 1
Solve: ? + 5 = 8. What number goes in the blank?
Difficulty: Beginner Time: ~3 minutes Skills: Basic Equation Solving
Definition:

Equation Solving: Finding the value that makes the equation true. An equation shows that two expressions are equal. The unknown (often shown as ? or a box) represents the number we need to find.

Note: To solve addition equations like ? + 5 = 8, we need to find what number plus 5 equals 8.

Step-by-step solving method:
  1. Identify the equation: ? + 5 = 8
  2. Think: What number plus 5 equals 8?
  3. Use subtraction to find the unknown: 8 - 5 = 3
  4. Check: 3 + 5 = 8 ✓
Original Equation
? + 5 = 8
Operation
8 - 5 = 3
Solution
? = 3
Step 1: Identify the equation

We have ? + 5 = 8

Step 2: Find the unknown

Think: ? + 5 = 8 means ? = 8 - 5

Step 3: Calculate

8 - 5 = 3

Step 4: Verify

Check: 3 + 5 = 8 ✓

? = 3
Final answer:

The number 3 goes in the blank

Applied rules:

• Equation Balance: Both sides must be equal

• Inverse Operation: Use subtraction to solve addition equations

• Verification: Always check your answer

• Practice Tip: Think of equations as balance scales

Related Examples:
  • ? + 3 = 7 → ? = 4 (because 7 - 3 = 4)
  • ? + 6 = 9 → ? = 3 (because 9 - 6 = 3)
  • ? + 2 = 5 → ? = 3 (because 5 - 2 = 3)
Quick Tips:
  • To solve ? + number = total, subtract: total - number = ?
  • Think of addition and subtraction as opposites
  • Always check your answer by substituting back
Frequently Asked Questions:

Q: Why do we subtract to solve addition equations?
A: Addition and subtraction are opposite operations. To find the unknown in ? + 5 = 8, we subtract 5 from both sides.

Q: Can I use counting to solve this?
A: Yes, you can count up from 5 to 8 to find the difference.

2 Basic Subtraction Equations
Exercise 2
Solve: 9 - ? = 4. What number goes in the blank?
Difficulty: Beginner Time: ~4 minutes Skills: Basic Equation Solving
Definition:

Subtraction Equation: An equation where one number minus the unknown equals another number. To solve 9 - ? = 4, we need to find what number subtracted from 9 gives 4.

Note: In subtraction equations, the unknown can be in different positions, requiring different solving strategies.

Step-by-step solving method:
  1. Identify the equation: 9 - ? = 4
  2. Think: 9 minus what number equals 4?
  3. Use subtraction to find the unknown: 9 - 4 = 5
  4. Check: 9 - 5 = 4 ✓
Original Equation
9 - ? = 4
Operation
9 - 4 = 5
Solution
? = 5
Step 1: Identify the equation

We have 9 - ? = 4

Step 2: Find the unknown

Think: 9 - ? = 4 means ? = 9 - 4

Step 3: Calculate

9 - 4 = 5

Step 4: Verify

Check: 9 - 5 = 4 ✓

? = 5
Final answer:

The number 5 goes in the blank

Applied rules:

• Equation Balance: Both sides must be equal

• Inverse Operation: Use subtraction to solve when unknown is subtracted

• Verification: Always check your answer

• Practice Tip: Think of equations as balance scales

Related Examples:
  • 7 - ? = 3 → ? = 4 (because 7 - 3 = 4)
  • 10 - ? = 6 → ? = 4 (because 10 - 6 = 4)
  • 8 - ? = 2 → ? = 6 (because 8 - 2 = 6)
Quick Tips:
  • To solve number - ? = result, subtract: number - result = ?
  • Think of subtraction and addition as opposites
  • Always check your answer by substituting back
Frequently Asked Questions:

Q: How is this different from ? - 4 = 5?
A: In 9 - ? = 4, we subtract the unknown from 9. In ? - 4 = 5, we subtract 4 from the unknown.

Q: Can I use addition to solve this?
A: Yes, 9 - ? = 4 is the same as ? + 4 = 9.

3 Balancing Operations
Exercise 3
If 4 + ? = 7, what is the value of 7 - 4?
Difficulty: Intermediate Time: ~5 minutes Skills: Balancing Operations
Definition:

Balancing Operations: Understanding that equations remain balanced when the same operation is performed on both sides. This concept helps us see the relationship between addition and subtraction.

Note: If 4 + ? = 7, then ? = 7 - 4. This shows how addition and subtraction are inverse operations.

Step-by-step solving method:
  1. Solve the first equation: 4 + ? = 7
  2. Find ? = 7 - 4 = 3
  3. Calculate 7 - 4 directly
  4. Notice the relationship between the operations
First Equation
4 + ? = 7
Unknown Value
? = 3
Second Calculation
7 - 4 = 3
Step 1: Solve the equation

4 + ? = 7 means ? = 7 - 4 = 3

Step 2: Calculate the second expression

7 - 4 = 3

Step 3: Observe the relationship

Both expressions equal 3

Step 4: Understand the principle

4 + ? = 7 and 7 - 4 = ? are related equations

7 - 4 = 3
Final answer:

7 - 4 = 3

Applied rules:

• Inverse Operations: Addition and subtraction are opposites

• Equation Balance: Operations maintain equality

• Relationship Recognition: Understanding related equations

• Practice Tip: See how operations relate to each other

Related Examples:
  • If 5 + ? = 9, then 9 - 5 = 4
  • If 3 + ? = 8, then 8 - 3 = 5
  • If 6 + ? = 10, then 10 - 6 = 4
Quick Tips:
  • Addition and subtraction are inverse operations
  • If a + ? = b, then b - a = ?
  • Understanding relationships helps solve equations faster
Frequently Asked Questions:

Q: Why do these operations give the same answer?
A: Because addition and subtraction are inverse operations that undo each other.

Q: Does this work for multiplication and division too?
A: Yes, they are also inverse operations.

Solutions: Exercises 4 to 5
4 Unknowns in Addition
Exercise 4
Find the missing number: 6 + ? = 10. Then verify your answer.
Definition:

Unknown in Addition: When solving equations of the form a + ? = b, we need to find what number added to 'a' gives 'b'. The unknown is found by subtracting: ? = b - a.

Note: Verification means checking that our solution makes the original equation true.

Step-by-step solving method:
  1. Identify the equation: 6 + ? = 10
  2. Find the unknown: ? = 10 - 6
  3. Calculate: ? = 4
  4. Verify: 6 + 4 = 10 ✓
Original Equation
6 + ? = 10
Solving
? = 10 - 6 = 4
Verification
6 + 4 = 10 ✓
Step 1: Identify the equation

We have 6 + ? = 10

Step 2: Find the unknown

? = 10 - 6 = 4

Step 3: Verify the solution

Substitute back: 6 + 4 = 10 ✓

Step 4: Conclusion

The missing number is 4

Missing number = 4
Final answer:

The missing number is 4, and 6 + 4 = 10

Applied rules:

• Equation Balance: Both sides must be equal

• Inverse Operation: Use subtraction to solve addition equations

• Verification: Always check your answer

• Practice Tip: Verification confirms your solution is correct

Related Examples:
  • 5 + ? = 9 → ? = 4 (verify: 5 + 4 = 9 ✓)
  • 3 + ? = 7 → ? = 4 (verify: 3 + 4 = 7 ✓)
  • 8 + ? = 12 → ? = 4 (verify: 8 + 4 = 12 ✓)
Quick Tips:
  • Always verify your answer by substituting back
  • To solve ? + a = b, calculate: b - a = ?
  • Verification is crucial for ensuring accuracy
Frequently Asked Questions:

Q: Why is verification important?
A: It confirms your answer is correct and helps catch calculation errors.

Q: What if verification doesn't work?
A: Go back and check your calculations - you made an error somewhere.

5 Unknowns in Subtraction
Exercise 5
Solve: ? - 3 = 5. What number goes in the blank?
Definition:

Unknown in Subtraction: When solving equations of the form ? - a = b, we need to find what number minus 'a' gives 'b'. The unknown is found by adding: ? = b + a.

Note: Unlike equations where the unknown is subtracted FROM a number, here we're finding what number had 'a' subtracted from it.

Step-by-step solving method:
  1. Identify the equation: ? - 3 = 5
  2. Find the unknown: ? = 5 + 3
  3. Calculate: ? = 8
  4. Verify: 8 - 3 = 5 ✓
Original Equation
? - 3 = 5
Solving
? = 5 + 3 = 8
Verification
8 - 3 = 5 ✓
Step 1: Identify the equation

We have ? - 3 = 5

Step 2: Find the unknown

? = 5 + 3 = 8

Step 3: Verify the solution

Substitute back: 8 - 3 = 5 ✓

Step 4: Conclusion

The missing number is 8

Missing number = 8
Final answer:

The number 8 goes in the blank

Applied rules:

• Equation Balance: Both sides must be equal

• Inverse Operation: Use addition to solve subtraction equations

• Verification: Always check your answer

• Practice Tip: Pay attention to the position of the unknown

Related Examples:
  • ? - 4 = 6 → ? = 10 (because 6 + 4 = 10)
  • ? - 2 = 7 → ? = 9 (because 7 + 2 = 9)
  • ? - 5 = 3 → ? = 8 (because 3 + 5 = 8)
Quick Tips:
  • To solve ? - a = b, calculate: b + a = ?
  • Position of the unknown changes the solving method
  • Always verify your answer by substituting back
Frequently Asked Questions:

Q: How is ? - 3 = 5 different from 8 - ? = 3?
A: In ? - 3 = 5, we're finding the starting number. In 8 - ? = 3, we're finding what was subtracted.

Q: Why do we add to solve a subtraction equation?
A: Addition and subtraction are inverse operations. To undo subtraction, we add.

Solutions: Exercises 6 to 10
6 Equation Verification
Exercise 6
Is 7 the solution to ? + 4 = 12? Show your work.
Definition:

Equation Verification: Checking whether a proposed solution makes the equation true by substituting the value back into the original equation and evaluating both sides.

Note: Verification is a crucial step in equation solving that confirms the accuracy of our solution.

Step-by-step verification method:
  1. Substitute the proposed solution into the equation
  2. Calculate the result of the substitution
  3. Compare the result to the other side of the equation
  4. Determine if both sides are equal
Proposed Solution
? = 7
Substitution
7 + 4 = 11
Comparison
11 ≠ 12
Step 1: Substitute the proposed solution

Replace ? with 7: 7 + 4 = 12

Step 2: Calculate the left side

7 + 4 = 11

Step 3: Compare both sides

Left side: 11, Right side: 12

Step 4: Determine if equal

Since 11 ≠ 12, 7 is not the solution

7 is not the solution
Final answer:

No, 7 is not the solution to ? + 4 = 12 because 7 + 4 = 11, not 12. The correct solution is 8.

Applied rules:

• Substitution Method: Replace variable with proposed value

• Equality Check: Both sides must be equal for valid solution

• Verification: Essential for confirming accuracy

• Practice Tip: Always verify solutions to avoid errors

Related Examples:
  • Is 5 solution to ? + 3 = 8? → 5 + 3 = 8 ✓ Yes
  • Is 6 solution to ? - 2 = 4? → 6 - 2 = 4 ✓ Yes
  • Is 9 solution to ? + 5 = 15? → 9 + 5 = 14 ≠ 15 No
Quick Tips:
  • Always substitute the proposed solution back into the original equation
  • Calculate each side separately
  • Compare the results to verify equality
Frequently Asked Questions:

Q: What if both sides are equal after substitution?
A: Then the proposed solution is correct.

Q: Do I always need to verify?
A: Yes, verification is essential to ensure accuracy.

7 Word Problems
Exercise 7
Tom has some marbles. He gives 3 marbles to his friend and now has 5 marbles left. How many marbles did Tom have at first?
Definition:

Word Problem to Equation: Converting a real-world scenario into a mathematical equation. Identify the unknown, the operations involved, and the relationship between quantities.

Note: In this problem, the unknown is the starting number of marbles, and we know that starting amount minus 3 equals 5.

Step-by-step problem-solving method:
  1. Identify the unknown: starting number of marbles
  2. Identify the operations: started with some, gave away 3, ended with 5
  3. Set up the equation: ? - 3 = 5
  4. Solve: ? = 5 + 3 = 8
  5. Verify: 8 - 3 = 5 ✓
Unknown
Starting marbles
Equation
? - 3 = 5
Solution
? = 8
Step 1: Identify the unknown

We need to find how many marbles Tom started with

Step 2: Identify the relationship

Starting amount - 3 given away = 5 remaining

Step 3: Set up the equation

? - 3 = 5

Step 4: Solve the equation

? = 5 + 3 = 8

Step 5: Verify the solution

8 - 3 = 5 ✓

Tom had 8 marbles at first
Final answer:

Tom had 8 marbles at first

Applied rules:

• Problem Translation: Convert words to mathematical expressions

• Variable Identification: Determine what the unknown represents

• Equation Setup: Create equation based on problem description

• Practice Tip: Break word problems into smaller steps

Related Examples:
  • Anna had some stickers. She used 4 and has 6 left → ? - 4 = 6 → Started with 10
  • Ben earned some money. He spent 5 and has 3 left → ? - 5 = 3 → Started with 8
  • Cara bought some apples. She ate 2 and has 7 left → ? - 2 = 7 → Started with 9
Quick Tips:
  • Identify the unknown first
  • Look for key words: "more," "less," "gave," "left"
  • Set up the equation based on the story
Frequently Asked Questions:

Q: How do I know whether to add or subtract?
A: Words like "gave," "used," "spent" indicate subtraction. Words like "got," "found," "earned" indicate addition.

Q: What if there are multiple operations?
A: Focus on the relationship between the beginning and end amounts.

8 Mixed Operations
Exercise 8
Solve: 9 - ? + 2 = 6. What number goes in the blank?
Definition:

Mixed Operations Equation: An equation containing multiple operations. To solve, perform operations in the correct order and isolate the unknown by performing inverse operations on both sides.

Note: In this equation, we can rearrange it as 9 + 2 - ? = 6, which simplifies to 11 - ? = 6.

Step-by-step solving method:
  1. Simplify the equation: 9 - ? + 2 = 6 becomes 11 - ? = 6
  2. Isolate the unknown: 11 - ? = 6
  3. Solve: ? = 11 - 6 = 5
  4. Verify: 9 - 5 + 2 = 4 + 2 = 6 ✓
Original Equation
9 - ? + 2 = 6
Simplified
11 - ? = 6
Solution
? = 5
Step 1: Simplify the equation

Combine constants: 9 + 2 = 11, so 11 - ? = 6

Step 2: Isolate the unknown

We have 11 - ? = 6

Step 3: Solve for the unknown

? = 11 - 6 = 5

Step 4: Verify the solution

Substitute back: 9 - 5 + 2 = 4 + 2 = 6 ✓

? = 5
Final answer:

The number 5 goes in the blank

Applied rules:

• Order of Operations: Perform operations correctly

• Simplification: Combine like terms when possible

• Isolation: Get the unknown by itself

• Practice Tip: Work step by step through mixed operations

Related Examples:
  • 7 - ? + 3 = 8 → 10 - ? = 8 → ? = 2
  • 6 + ? - 4 = 5 → 2 + ? = 5 → ? = 3
  • 8 - ? + 1 = 4 → 9 - ? = 4 → ? = 5
Quick Tips:
  • Simplify by combining constants first
  • Work step by step through operations
  • Always verify your answer by substituting back
Frequently Asked Questions:

Q: What if the equation is more complex?
A: Break it down into simpler steps and work through operations one at a time.

Q: Can I rearrange the terms?
A: Be careful - only rearrange terms when you maintain the same operations.

9 Real-Life Applications
Exercise 9
A baker made some cookies. He sold 6 cookies and now has 9 cookies left. Write an equation and solve for how many cookies he made originally.
Definition:

Real-Life Equation Applications: Using equations to solve practical problems. Identify the unknown quantity, set up an equation based on the situation, solve it, and interpret the result in context.

Note: In this problem, we're finding the original number of cookies before any were sold.

Step-by-step problem-solving method:
  1. Identify the unknown: original number of cookies
  2. Identify the relationship: original - sold = remaining
  3. Set up the equation: ? - 6 = 9
  4. Solve: ? = 9 + 6 = 15
  5. Interpret: The baker made 15 cookies originally
Unknown
Original cookies
Equation
? - 6 = 9
Solution
? = 15
Step 1: Identify the unknown

We need to find the original number of cookies

Step 2: Identify the relationship

Original cookies - 6 sold = 9 remaining

Step 3: Set up the equation

? - 6 = 9

Step 4: Solve the equation

? = 9 + 6 = 15

Step 5: Interpret the result

The baker originally made 15 cookies

Original cookies = 15
Final answer:

The baker made 15 cookies originally

Applied rules:

• Problem Modeling: Translate real situations into equations

• Variable Representation: Assign unknown to the quantity we seek

• Contextual Interpretation: Understand the meaning of the solution

• Practice Tip: Connect math to everyday experiences

Related Examples:
  • Books on shelf: ? - 3 = 7 → Originally 10 books
  • Money saved: ? - 5 = 12 → Originally $17
  • Gardening: ? - 4 = 6 → Originally 10 plants
Quick Tips:
  • Identify what you're trying to find
  • Translate the situation into an equation
  • Check if your answer makes sense in the context
Frequently Asked Questions:

Q: How do I know what operation to use?
A: Look for key words that indicate addition or subtraction.

Q: What if my answer doesn't make sense?
A: Recheck your equation setup and calculations.

10 Problem Solving
Exercise 10
Sarah had some stickers. She gave 4 stickers to her friend and then found 3 more stickers. Now she has 8 stickers. How many stickers did Sarah have at the beginning?
Definition:

Multi-Step Equation Problem: Problems that involve multiple operations in sequence. The equation reflects the series of events: starting amount minus given amount plus found amount equals final amount.

Note: This problem requires setting up an equation with multiple operations: ? - 4 + 3 = 8.

Step-by-step problem-solving method:
  1. Identify the unknown: starting number of stickers
  2. Track the sequence of operations: start - 4 + 3 = 8
  3. Simplify: start - 1 = 8
  4. Solve: start = 8 + 1 = 9
  5. Verify: 9 - 4 + 3 = 5 + 3 = 8 ✓
Sequence
? - 4 + 3 = 8
Simplified
? - 1 = 8
Solution
? = 9
Step 1: Identify the unknown

We need to find the starting number of stickers

Step 2: Set up the equation

Starting - 4 (given) + 3 (found) = 8 (final)

Step 3: Simplify the equation

? - 4 + 3 = ? - 1 = 8

Step 4: Solve for the unknown

? = 8 + 1 = 9

Step 5: Verify the solution

9 - 4 + 3 = 5 + 3 = 8 ✓

Sarah started with 9 stickers
Final answer:

Sarah had 9 stickers at the beginning

Applied rules:

• Multi-Step Problems: Track each operation in sequence

• Equation Setup: Represent the sequence of events mathematically

• Simplification: Combine like terms when possible

• Verification: Check the entire sequence matches the problem

Related Examples:
  • Money: ? - 5 + 2 = 10 → Started with 13
  • Toys: ? - 3 + 4 = 9 → Started with 8
  • Books: ? - 2 + 1 = 6 → Started with 7
Quick Tips:
  • Track each operation in the order it happened
  • Simplify by combining constants when possible
  • Always verify by following the entire sequence
Frequently Asked Questions:

Q: How do I handle multiple operations?
A: Follow the sequence as described in the problem.

Q: What if the problem is confusing?
A: Break it down into individual steps and represent each with math.

Key Laws, Methods, Rules, and Definitions
\(? + a = b \Rightarrow ? = b - a\)
Addition Equation
Key definitions:

Equation: A mathematical statement showing that two expressions are equal, using an equals sign (=).

Unknown: A number we don't know, represented by a symbol like ?, □, or a letter.

Solution: The value that makes the equation true when substituted for the unknown.

Inverse Operations: Operations that undo each other, like addition and subtraction.

Complete methodology:
  1. Identify the unknown: Determine what value needs to be found
  2. Set up the equation: Write the mathematical relationship
  3. Isolate the unknown: Use inverse operations to get the unknown alone
  4. Solve: Calculate the value of the unknown
  5. Verify: Check that the solution makes the equation true
Tip 1: Addition and subtraction are inverse operations.
Tip 2: To solve ? + a = b, subtract: ? = b - a.
Tip 3: To solve ? - a = b, add: ? = b + a.
Tip 4: Always verify your solution by substituting back.
Common errors: Forgetting to verify solutions, applying wrong inverse operation, not following order of operations in mixed problems.
Exam preparation: Practice identifying unknowns, setting up equations from word problems, solving equations with inverse operations, verifying solutions.
Rules to remember:

• Equation Balance: Whatever you do to one side, do to the other

• Inverse Operations: Addition undoes subtraction and vice versa

• Verification: Always check your solution by substitution

• Problem Translation: Convert words to mathematical expressions

Rules and Methods for Equation Solving
\(? - a = b \Rightarrow ? = b + a\)
Subtraction Equation
Addition
\(? + a = b\)
Solution: ? = b - a
Subtraction
\(? - a = b\)
Solution: ? = b + a
Verification
Substitute and check
Both sides must be equal

Key Takeaways

  • Identify the unknown value in the equation
  • Use inverse operations to isolate the unknown
  • Addition equations: subtract the same number from both sides
  • Subtraction equations: add the same number to both sides
  • Always verify your solution by substituting back
  • Convert word problems to mathematical equations
Detailed Summary: Understanding Solving Equations
Complete Concept Overview:

Understanding equation solving involves learning to find unknown values that make mathematical statements true. Students learn to identify unknowns, set up equations based on relationships, apply inverse operations to isolate variables, and verify their solutions. This foundational skill prepares students for more advanced algebraic thinking.

Core Rules and Principles:
  1. Equation Balance: Both sides of an equation must remain equal
  2. Inverse Operations: Addition and subtraction undo each other
  3. Isolation Strategy: Use inverse operations to get the unknown alone
  4. Verification: Always check solutions by substitution
  5. Problem Translation: Convert real-world situations to mathematical equations
Progressive Examples (Simple to Advanced):
Basic Level:

Addition Equation: ? + 3 = 7 → ? = 7 - 3 = 4

Subtraction Equation: 8 - ? = 3 → ? = 8 - 3 = 5

Verification: 4 + 3 = 7 ✓

Intermediate Level:

Unknown Subtraction: ? - 4 = 6 → ? = 6 + 4 = 10

Verification Required: Is 5 solution to ? + 2 = 8? → 5 + 2 = 7 ≠ 8, so no

Word Problem: Started with ?, gave 3, have 4 left → ? - 3 = 4 → ? = 7

Advanced Level:

Mixed Operations: 9 - ? + 2 = 6 → 11 - ? = 6 → ? = 5

Multi-Step Problem: Started with ?, gave 4, found 3, now have 8 → ? - 4 + 3 = 8 → ? = 9

Complex Verification: Check entire sequence of operations

Tips, Tricks, and Common Pitfalls:
  • Memorization Tip: "To find the unknown, do the opposite of what's happening to it"
  • Visualization Trick: Think of equations as balance scales that must stay equal
  • Common Mistake: Forgetting to verify solutions
  • Operation Strategy: Addition equations → subtract to solve; Subtraction equations → add to solve
  • Checking Work: Always substitute the solution back into the original equation
Key Notes for Long-Term Retention:
  • Equations express equality between two expressions
  • Inverse operations help isolate unknowns
  • Addition and subtraction are opposites
  • Verification ensures accuracy
  • Word problems require translation to mathematical form
  • Position of unknown affects solution strategy
Additional Memory Aids:
  • "What you do to one side, do to the other" - maintaining balance

Questions & Answers

Question: Why do I need to check my answer? Isn't solving the equation enough?

Answer: Checking your answer is extremely important! Here's why:

  • You might make a calculation error while solving
  • Checking confirms your answer is correct
  • It helps build good mathematical habits
  • It catches mistakes before they cause problems later

Think of it like double-checking your work on a test - it ensures accuracy!

Question: How can I help my child understand equations better?

Answer: Here are effective ways to help:

  • Use physical objects like blocks or counters to demonstrate equations
  • Relate equations to real-life situations (sharing toys, spending money)
  • Emphasize the importance of verification
  • Practice with simple equations first, then gradually increase difficulty
  • Encourage your child to explain their thinking

Making equations tangible helps children understand the abstract concepts.

Question: Why do I subtract when solving ? + 5 = 8 but add when solving ? - 3 = 5?

Answer: Great question! This happens because addition and subtraction are opposite operations:

  • In ? + 5 = 8, the 5 is being ADDED to the unknown, so we SUBTRACT 5 to undo it
  • In ? - 3 = 5, the 3 is being SUBTRACTED from the unknown, so we ADD 3 to undo it
  • We always do the OPPOSITE of what's happening to the unknown

Think of it like undoing actions: if you added something, you take it away to go back to where you started.

Math Glossary

Equation
A mathematical statement showing that two expressions are equal, using an equals sign (=).
Unknown
A number we don't know, represented by a symbol like ?, □, or a letter.
Solution
The value that makes the equation true when substituted for the unknown.
Inverse Operations
Operations that undo each other, like addition and subtraction.
Verification
The process of checking that a solution makes the original equation true.

Equation Solving Educational Team

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