Students can go through AP 7th Class Maths Notes Chapter 4 Simple Equations to understand and remember the concepts easily.
Class 7 Maths Chapter 4 Notes Simple Equations
→ A variable takes on different numerical values, its value is not fixed.
→ Variables are denoted by lower case letters like a, b, c, d, e, f, ……….. x, v, z, etc.
→ We can form expressions from variables.
→ The expressions are formed by performing operations like addition, subtraction, multiplication and division on the variables.
Examples:
- 14x – 5, the variable is x.
- 7p – \(\frac{9}{2}\), the variable is p
- abc + 1, the variables are a, b, c.
→ The value of an expression depends upon the given value of the variable.
Examples:
1) Find the value of 7x + 1 at x = 1
Solution:
7x + 1
x = 1
7(1) + 1 = 7 + 1 = 8
2) Find the value of 1 – 9x at x = – 2
Solution:
1 – 9x
x = – 2
1 – 9(-2) = 1 + 18 = 19
→ Zero of the expression : The value for which the expression becomes zero is called zero of the expression.
Ex: 1) Find the zero of 3x – 6
Solution:
Method 1 :
3x – 6 = 0
3x = 6
x = \(\frac{6}{3}\)
x = 2 is the zero of 3x – 6.
Method 2 :
Trial and error
Let x = 1
3(1) – 6 = 3 – 6 = -3
Let x = – 1
3(- 1) – 6 = – 3 – 6 = – 9
Let x = 2
3(2) – 6 = 6 – 6 = 0
∴ 2 is the zero of 3x – 6.
→ The zero of ax + b is \(\frac{-b}{a}\)
→ Equation : In an equation there is always an equality. The equality sign shows that the value of the expression to the left of the sign (LHS) is equal to the value of the expression to the right of the sign (RHS).
Ex : 1) 4x + 5 = 9
LHS = 4x + 5 RHS = 9
2) 94 = 7p – \(\frac{3}{7}\)
LHS = 94 RHS = 7p – \(\frac{3}{7}\)
RHS = 7p – –
→ An equation is a condition on a variable.
→ The condition is that two expressions should have equal value.
Note : At least one of the two expressions must contain the variable.
→ An equation remains same, when the , expression on the left and on the right are interchanged.
Ex: 6x + 1 = 9 – 4x
6x – 9 = – 4x – 1
→ In an equation LHS = RHS
→ The value of the equation which satisfies the given equation is called solution of the equation.
Ex : 1) Find the solution to x – 1 = 1
Solution:
x – 1 = 1
x = 1 + 1
x = 2
2 is the solution of x – 1 = 1.
Ex: 2) Is – 1 a solution to 2x – 1 = 0
Solution:
2x – 1 = 0
Let x = – 1
LHS : 2(- 1) – 1 = – 2 – 1 = – 3
RHS = 0
∴ LHS ≠ RHS
∴ – 1 is not the solution to 2x – 1 = 0
→ The highest number of variables present in an expression is called its degree.
Examples:
1) Degree of 2a – 1 is 1
2) Degree of 9a2 – 3 is 2
3) Degree of 1 – xyz = 3.
→ A simple equation will have always degree 1
Ex: Degree of 9 – 4x = 0 is 1.