Class 7 Maths Simple Equations Notes

Introduction:

The chapter “Simple Equations” in Class 7 Maths introduces students to the concept of equations and the process of solving them. An equation is a mathematical statement that shows the equality of two expressions. This chapter helps students understand how to solve simple equations with one variable, which is fundamental for solving more complex mathematical problems in the future.

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Key Concepts Covered:

1. What is an Equation?

• An equation is a mathematical statement that expresses the equality of two expressions separated by an equal sign (=).
• Example:
  • $2x + 5 = 11$2x+5=11
• Here, $2x + 5$2x+5 and $11$11 are two expressions, and the equal sign shows that both sides are equal.

2. What is a Simple Equation?

• A simple equation is an equation that contains one variable and can be solved using basic algebraic operations (addition, subtraction, multiplication, division).
• Example:
  • $x + 3 = 7$x+3=7
• The goal is to find the value of $x$x that makes the equation true.

3. Solving Simple Equations:

• Solving an equation means finding the value of the variable that makes both sides of the equation equal.
• Steps to solve a simple equation:
  1. Isolate the variable: Move all terms involving the variable to one side of the equation.
  2. Simplify: Perform the necessary arithmetic operations to solve for the variable.

Example 1: Solve $x + 5 = 12$x+5=12.

• Subtract 5 from both sides: $$x + 5 – 5 = 12 – 5 \quad \Rightarrow \quad x = 7$$x+5−5=12−5⇒x=7

Example 2: Solve $3x = 15$3x=15.

• Divide both sides by 3: $$\frac{3x}{3} = \frac{15}{3} \quad \Rightarrow \quad x = 5$$33x​=315​⇒x=5

4. Properties of Simple Equations:

• Balance Property: In an equation, both sides must remain equal. When you perform an operation on one side of the equation, you must perform the same operation on the other side to keep the equation balanced.
  • Example: If $x + 4 = 10$x+4=10, subtracting 4 from both sides gives $x = 6$x=6.
• Inverse Operations: You can use inverse operations (addition ↔ subtraction, multiplication ↔ division) to simplify equations and solve for the variable.
  • Example: In the equation $4x = 20$4x=20, divide both sides by 4 to isolate $x$x: $x = \frac{20}{4} = 5$x=420​=5.

5. Verifying Solutions:

• Once you solve the equation, it’s important to verify the solution by substituting the value of the variable back into the original equation.
  • Example: If $x = 7$x=7 is the solution to $x + 5 = 12$x+5=12, substitute $7$7 into the original equation: $$7 + 5 = 12 \quad \text{which is true.}$$7+5=12which is true.

6. Applications of Simple Equations:

• Simple equations are used to solve real-life problems that involve relationships between different quantities.
• Example: If you have 3 more than a certain number, and the total is 8, you can express this as the equation $x + 3 = 8$x+3=8, and solve for $x$x.

7. Word Problems Involving Simple Equations:

• Word problems often involve translating the information into an equation.
• Example:
  • “A number is increased by 7, and the result is 15. Find the number.”
  • Solution: Let the unknown number be $x$x. The equation is: $$x + 7 = 15$$x+7=15
  • Subtract 7 from both sides: $$x = 15 – 7 = 8$$x=15−7=8

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Important Questions with Answers:

1. What is an equation?
   • Answer: An equation is a mathematical statement that shows the equality of two expressions separated by an equal sign.
2. What is a simple equation?
   • Answer: A simple equation is an equation that contains one variable and can be solved by performing basic operations such as addition, subtraction, multiplication, or division.
3. How do you solve the equation x+5=12x + 5 = 12x+5=12?
   • Answer: Subtract 5 from both sides to get $x = 7$x=7.
4. What is the solution to 3x=153x = 153x=15?
   • Answer: Divide both sides by 3 to get $x = 5$x=5.
5. What does the balance property of equations state?
   • Answer: The balance property states that both sides of an equation must remain equal. Any operation performed on one side must be performed on the other side to maintain equality.
6. How do you verify the solution to an equation?
   • Answer: Substitute the value of the variable into the original equation and check if both sides are equal.
7. How do you solve the word problem: “A number is increased by 4, and the result is 10. Find the number.”
   • Answer: Let the unknown number be $x$x. The equation is $x + 4 = 10$x+4=10. Subtract 4 from both sides to get $x = 6$x=6.