Simple Equations

Quick Revision Notes: Class 7 Mathematics

Chapter: Simple Equations

1. What is an Equation?

• Definition: An equation is a condition on a variable. It is a mathematical statement that shows the equality of two expressions, separated by the sign of equality (=).
• Example: 4x + 5 = 65
• LHS and RHS:
  • LHS (Left Hand Side): The expression on the left side of the equality sign. (e.g., 4x + 5)
  • RHS (Right Hand Side): The expression on the right side of the equality sign. (e.g., 65)

2. What is a "Simple Equation"?

• An equation is a Simple Equation (or Linear Equation in one variable) if the highest power of the variable present in the equation is 1.
• Example: 2x - 3 = 7 is a simple equation because the power of x is 1.
• Non-Example: x^2 + 2x = 3 is not a simple equation because the power of x is 2.

3. Solution of an Equation

• Definition: The value of the variable for which the LHS becomes equal to the RHS is called the solution or root of the equation.
• Satisfying the equation: When we substitute the solution into the equation, LHS = RHS. This is called checking the result.

4. Rules for Solving a Simple Equation

To find the value of the unknown variable, we perform mathematical operations in such a way that the variable is isolated on one side.

• Rule 1 (Addition): The same number can be added to both sides of an equation.
• Rule 2 (Subtraction): The same number can be subtracted from both sides of an equation.
• Rule 3 (Multiplication): Both sides of an equation can be multiplied by the same non-zero number.
• Rule 4 (Division): Both sides of an equation can be divided by the same non-zero number.

5. Transposition Method ( पक्षांतरण )

Moving a term from one side of the equation to the other side with a change of sign is called transposition.

• Addition becomes Subtraction: If x + b = c, then x = c - b
• Subtraction becomes Addition: If x - b = c, then x = c + b
• Multiplication becomes Division: If a * x = c, then x = c / a
• Division becomes Multiplication: If x / a = c, then x = c * a

6. Formation of Equation from Statements (Word Problems)

To solve word problems, translate the given statements into mathematical expressions:

• "Sum of x and 5 is 12" $\rightarrow$ x + 5 = 12
• "7 subtracted from y is 3" $\rightarrow$ y - 7 = 3
• "4 times a number x is 20" $\rightarrow$ 4x = 20
• "One-third of a number p is 5" $\rightarrow$ p / 3 = 5
• "2 more than 3 times x is 11" $\rightarrow$ 3x + 2 = 11

Important Tips for MP Board Exam

1. Always write LHS and RHS clearly when checking your answers.
2. Do not forget to include the units in word problems (e.g., cm, kg, rupees).
3. Maintain the equality sign (=) in a straight vertical line while solving steps downward.