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Published 2026-08-26•Chapter: Simple Equations

Simple Equations - Formulation and solving of simple linear equations

Class 7 Mathematics: Simple Equations

Hello students! Welcome to today's fun and easy-to-understand math tutorial. Today, we are going to explore Simple Equations from your NCERT Class 7 syllabus.

Have you ever wondered how detectives solve mysteries by finding missing clues? In mathematics, an equation is just like a detective puzzle where we need to find a missing number!

By the end of this lesson, you will be able to:

  • Understand what an equation is.
  • Turn real-world word problems into mathematical equations (Formulation).
  • Find the value of the unknown variable (Solving).

    • Let's dive in!

    ---

    1. The Big Picture: The Weighing Balance Analogy

    Imagine a traditional vegetable vendor's weighing scale (*Tarazu*).

    ```

    [ Left Pan ] === (Equal Balance) === [ Right Pan ]

    ```

  • For the scale to remain balanced, the weight on the Left-Hand Side (LHS) must be equal to the weight on the Right-Hand Side (RHS).
  • If you add a $1\text{ kg}$ weight to the left pan, the balance tips! To bring it back to balance, you must add $1\text{ kg}$ to the right pan too.
  • Similarly, if you remove weight from one side, you must remove the exact same weight from the other side.

    • An equation works on the exact same logic! An equation is simply a statement that shows two mathematical expressions are equal, joined by an equal sign ($=$).

    ---

    2. What Makes Up an Equation?

    Before we start building equations, let's learn the basic building blocks:

  • Variable: A letter (like $x, y, z, m, p$) that represents an unknown number. Its value can change (vary).
  • Constant: A fixed numerical value that never changes (like $5, 12, -3$).
  • Algebraic Expression: A combination of variables, constants, and operations ($+, -, \times, \div$).

    • * *Example:* $2x + 3$

  • Equation: When we set an expression equal to a value or another expression using an equal sign ($=$).

    • * *Example:* $2x + 3 = 11$

    > 💡 Teacher's Note: An equation MUST always have an equal sign ($=$). Without an equal sign, $2x + 3$ is just an *expression*, not an equation!

    ---

    3. Step 1: Formulating Equations from Word Statements

    Formulating an equation means converting everyday English sentences into mathematical statements.

    Simple Rules to Translate Words into Math:

  • *"Sum of..."* or *"added to"* $\rightarrow \mathbf{+}$
  • *"Difference of..."* or *"subtracted from"* $\rightarrow \mathbf{-}$
  • *"Times..."* or *"product of"* $\rightarrow \mathbf{\times}$
  • *"Divided by..."* or *"one-third of"* $\rightarrow \mathbf{\div}$
  • *"Is..."*, *"gives..."*, or *"results in..."* $\rightarrow \mathbf{=}$

    • Let's See Some Examples:

    | Word Statement | Step-by-Step Translation | Algebraic Equation |

    | :--- | :--- | :--- |

    | 1. The sum of a number $x$ and $4$ is $12$. | Add $4$ to $x$ to get $12$. | $x + 4 = 12$ |

    | 2. $7$ times a number $m$ minus $3$ gives $18$. | Multiply $m$ by $7$, then subtract $3$. | $7m - 3 = 18$ |

    | 3. One-fifth of a number $y$ is $6$. | Divide $y$ by $5$ to equal $6$. | $\frac{y}{5} = 6$ |

    ---

    4. Step 2: Solving Simple Equations

    Solving an equation means finding the exact numerical value of the variable that makes the Left Hand Side (LHS) = Right Hand Side (RHS). This value is called the solution or root of the equation.

    There are two primary methods to solve an equation:

    Method A: The Balancing Method

    Just like a weighing scale, whatever operation you perform on the Left-Hand Side, you must perform the exact same operation on the Right-Hand Side.

    Example: Solve $x + 5 = 12$

  • Goal: Keep $x$ alone on the LHS.
  • Problem: There is an extra $+ 5$ attached to $x$.
  • Action: Subtract $5$ from both sides.

    • $$x + 5 - 5 = 12 - 5$$

    $$x = 7$$

    ---

    Method B: The Transposition Method (Fast & Easy!)

    Transposition means moving a term from one side of the equal sign ($=$) to the other side. When a term crosses the equal sign bridge, its sign flips to its opposite operation:

  • Plus ($+$) becomes Minus ($-$)
  • Minus ($-$) becomes Plus ($+$)
  • Multiplication ($\times$) becomes Division ($\div$)
  • Division ($\div$) becomes Multiplication ($\times$)

    • #### Let's walk through an example using Transposition:

    Solve: $3y - 7 = 14$

  • Step 1: Move the constant term ($-7$) across the equal sign.

    • Since it is $-7$, moving it to the RHS changes it to $+7$.

    $$3y = 14 + 7$$

    $$3y = 21$$

  • Step 2: Move the multiplier ($3$) across the equal sign.

    • Since $3$ is multiplied by $y$, moving it to the RHS changes it to division by $3$.

    $$y = \frac{21}{3}$$

    $$y = 7$$

    Answer: $y = 7$

    ---

    Practice Corner: Guided Questions with Detailed Solutions

    Now, let's put our learning into action with 3 classic NCERT-style practice questions!

    ---

    Question 1: Formulation & Solving

    Statement: *"If you subtract $6$ from $6$ times a number $n$, you get $60$."*

    Task: Formulate the equation and solve for $n$.

    #### Solution:

  • Step 1: Formulate the equation.

    • * $6$ times a number $n$ = $6n$

    * Subtracting $6$ from $6n$ = $6n - 6$

    * The result is $60$, so set it equal to $60$:

    $$\mathbf{6n - 6 = 60}$$

  • Step 2: Solve the equation using Transposition.

    • * Move $-6$ to the RHS (it becomes $+6$):

    $$6n = 60 + 6$$

    $$6n = 66$$

    * Move $6$ (multiplier) to the RHS (it becomes a divisor):

    $$n = \frac{66}{6}$$

    $$n = 11$$

    Final Answer: The equation is $6n - 6 = 60$, and the value of $n$ is $11$.

    ---

    Question 2: Solving Equations with Brackets

    Solve the equation: $4(m + 3) = 20$

    #### Solution:

  • Step 1: Simplify or transpose the multiplier outside the bracket.

    • The number $4$ is multiplied with the entire bracket $(m + 3)$. Move $4$ to the RHS as a division:

    $$m + 3 = \frac{20}{4}$$

    $$m + 3 = 5$$

  • Step 2: Isolate the variable $m$.

    • Move $+3$ to the RHS (it becomes $-3$):

    $$m = 5 - 3$$

    $$m = 2$$

  • Step 3: Check your answer (Verification).

    • Substitute $m = 2$ back into the LHS:

    $$\text{LHS} = 4(2 + 3) = 4(5) = 20 = \text{RHS}$$

    Since $\text{LHS} = \text{RHS}$, our answer is correct!

    Final Answer: $m = 2$

    ---

    Question 3: Real-World Word Problem

    Problem: *Rohan's father is $45$ years old. He is $3$ years older than three times Rohan's age. Find Rohan's age.*

    #### Solution:

  • Step 1: Define the unknown variable.

    • Let Rohan's age be $x$ years.

  • Step 2: Formulate the equation based on the condition.

    • * Three times Rohan's age = $3x$

    * Father is $3$ years older than $3x$ = $3x + 3$

    * Father's actual age = $45$

    * Setting up the equation:

    $$\mathbf{3x + 3 = 45}$$

  • Step 3: Solve the equation.

    • * Transpose $+3$ to the RHS:

    $$3x = 45 - 3$$

    $$3x = 42$$

    * Transpose $3$ to the RHS:

    $$x = \frac{42}{3}$$

    $$x = 14$$

    Final Answer: Rohan's age is $14$ years.

    ---

    Summary Checklist for Revision

  • Equation: LHS = RHS statement containing a variable.
  • Formulation: Read carefully $\rightarrow$ identify unknown as variable $\rightarrow$ translate words into operations.
  • Transposition Rules:

    • * $+ \rightarrow -$

    * $- \rightarrow +$

    * $\times \rightarrow \div$

    * $\div \rightarrow \times$

    Keep practicing, stay curious, and remember: math is just a game of rules! You've got this!