What is an Expression and an Equation in Mathematics?

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🧮 What is an Expression and an Equation in Mathematics? (With Examples)

Understanding the difference between expressions and equations is a key concept in algebra and middle school math. These terms are often used in mathematics to represent values and relationships between variables and numbers.

📘 Definition

🔹 Expression in Math:

An expression is a mathematical phrase that includes numbers, variables (like x or y), and operation symbols such as +, −, ×, or ÷.
👉 It does not include an equal (=) sign.

🔸 Examples of Expressions:

  • 5x

  • 2x − 3

  • 3x + 2

  • 2xy + 5

  • xyz + x + y + z

  • x² + 1

  • y² + y

🔹 Equation in Math:

An equation is a mathematical statement where two expressions are equal to each other, connected by an equal (=) sign.

🔸 Examples of Equations:

  • 5x = 25

  • 2x − 3 = 9

  • (2y + 5)/2 = 37/2

  • 6z + 10 = -2

✅ Key Difference Between Expressions and Equations

FeatureExpressionEquation
DefinitionA combination of numbers, variables, and operations.A statement that shows equality between two expressions.
Equal Sign❌ Not used✅ Must have an "=" sign
SidesOnly one sideHas two sides: LHS and RHS
ResultSimplified valueSolved for variable(s)
Example7x − 2(3x + 14)7x − 5 = 19

🧠 Understanding Equations and How to Solve Them

An algebraic equation always includes an equality sign (=).

  • The left side of the equation is called the LHS (Left Hand Side).

  • The right side is the RHS (Right Hand Side).
    An equation is true only when the values on both sides are equal for a certain variable.

🔸 Example:

Given: 2x − 3 = 7

To find the solution:

  • Add 3 to both sides: 2x = 10

  • Divide by 2: x = 5

✔️ So, x = 5 is the solution, because:

  • LHS = 2 × 5 − 3 = 10 − 3 = 7

  • RHS = 7

❌ Example of Non-solution:

Try x = 10:

  • LHS = 2 × 10 − 3 = 17

  • RHS = 7
    Since 17 ≠ 7, x = 10 is not a solution.

🛠️ How to Solve Algebraic Equations

Tip: Think of an equation like a balanced scale.
➡️ Whatever operation you do on one side, you must do the same on the other side to keep the balance.

Steps to solve:

  1. Simplify both sides (if needed).

  2. Use inverse operations to isolate the variable.

  3. Check your solution by substituting the value back into the original equation.

📚 Summary

  • A math expression represents a value and includes numbers, variables, and operators.

  • A math equation shows equality and has two expressions on either side of an equal sign.

  • You simplify expressions but solve equations.

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