Solve:

Step-by-step solution with detailed explanations and verification

Problem

Solve for x

Step-by-Step Solution

1

Original equation

✓

Subtract 25 from both sides

Final Answer

Solution:

Verification

Substitute x = 15 into the original equation: 15 + 25 = 40 ✓

Practice with Similar Problems

Problem 1

x + 30 = 45

Problem 2

x + 28 = 43

Problem 3

x + 22 = 37

Understanding Linear Equations

📐 What is a Linear Equation?

A linear equation is an equation where the highest power of the variable is 1. The equation x + 25 = 40 is linear because x appears only to the first power.

  • • Has exactly one variable (typically x)
  • • Variable is raised to the first power only
  • • Graphs as a straight line
  • • Usually has exactly one solution

⚖️ The Balance Principle

Think of an equation like a balanced scale. Whatever you do to one side, you must do to the other to keep it balanced.

  • • Add the same number to both sides ✓
  • • Subtract the same number from both sides ✓
  • • Multiply both sides by the same number ✓
  • • Divide both sides by the same number ✓

General Strategy for Solving Equations

1

Simplify Each Side

Remove parentheses using the distributive property and combine like terms on each side.

2

Collect Variable Terms

Use addition or subtraction to get all variable terms on one side and constants on the other.

3

Isolate the Variable

Use multiplication or division to get the variable alone with a coefficient of 1.

4

Check Your Answer

Always substitute your solution back into the original equation to verify it works!

Frequently Asked Questions

What is the solution to x + 25 = 40?▼
The solution is x = 15. This means when you substitute this value for x in the original equation, both sides will be equal.
How do I know if my answer is correct?▼
Substitute your answer back into the original equation. If both sides are equal, your answer is correct. For this equation: Substitute x = 15 into the original equation: 15 + 25 = 40 ✓
What are inverse operations?▼
Inverse operations are operations that "undo" each other. Addition and subtraction are inverses (adding 5 is undone by subtracting 5). Multiplication and division are inverses (multiplying by 3 is undone by dividing by 3). We use inverse operations to isolate the variable.
Why do we need to balance both sides?▼
An equation states that two expressions are equal. If we only change one side, they would no longer be equal, and we'd lose the relationship we're trying to solve. By doing the same operation to both sides, we maintain the equality while transforming the equation into a simpler form.
Can a linear equation have no solution or infinite solutions?▼
Yes! Most linear equations have exactly one solution, but some are special cases. An equation like "x + 1 = x + 2" has no solution (it's a contradiction). An equation like "2x = x + x" is true for all values of x (it's an identity). The equation x + 25 = 40 has exactly one solution: x = 15.
What if the answer is a fraction or decimal?▼
Many equations have fractional or decimal solutions—that's completely normal! You can express the answer as a fraction (often preferred in algebra) or as a decimal. Both are correct as long as they represent the same value.

How to Solve x + 25 = 40

Solving the equation x + 25 = 40 is a fundamental algebra problem that helps students understand linear equations and the concept of isolating variables. This type of equation appears frequently in middle school and high school mathematics, and mastering it builds a strong foundation for more advanced algebraic concepts.

Understanding the Equation

The equation x + 25 = 40 is a linear equation in one variable (x). Our goal is to find the value of x that makes both sides of the equation equal. By following systematic algebraic steps—such as combining like terms, using inverse operations, and maintaining balance—we can determine that x = 15.

Key Concepts

  • Inverse Operations: Use opposite operations to isolate the variable (addition ↔ subtraction, multiplication ↔ division)
  • Balance Method: Whatever you do to one side of the equation, do to the other side to maintain equality
  • Order of Operations: Follow PEMDAS/BODMAS when simplifying expressions
  • Verification: Always check your answer by substituting it back into the original equation

Why This Matters

Learning to solve equations like x + 25 = 40 is essential for success in algebra and beyond. These skills are used in science, engineering, economics, and everyday problem-solving. Whether you're calculating distances, determining costs, or analyzing data, the ability to set up and solve equations is invaluable.

Common Mistakes to Avoid

  • ✗Forgetting to perform the same operation on both sides of the equation
  • ✗Making arithmetic errors when combining like terms or calculating
  • ✗Skipping the verification step to check if your solution is correct
  • ✗Rushing through steps without understanding the underlying concepts

Tips for Success

  • ✓Write out each step clearly to avoid confusion and track your work
  • ✓Practice regularly with similar problems to build confidence and speed
  • ✓Always verify your answer by substituting it back into the original equation
  • ✓Understand the "why" behind each step, not just the mechanical process

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