Constants and variables
Linear equations in one variable of Class 8
CONSTANTS AND VARIABLES:
A CONSTANT is a quantity whose value remains the same throughout a particular problem.
A VARIABLE is a quantity whose value is free to vary.
e.g.
Question 1. x + 1 = 2 and
Question 2. 2y + 3 = 5
Solution: In 1 above, x + 1 is an algebraic expression in the variable x. we read it as “ x plus 1 is equal to 2”. x is some number, called variable.
Solution: In 2 above, 2y + 3 is an algebraic expression in the variable y, we read it as “ 2 times y or 2y plus 3 is equal to 5”. y is some number, called variable.
There are two kinds of constants-fixed and arbitrary. Numbers such as 7, -3, 1/2, and p are examples of FIXED constants. Their values never change. In 5x + 7 = 0, the numbers 0, 5, and 7, are fixed constants.
ARBITRARY
constants can be assigned different values for different problems. Arbitrary constants are indicated by letters-quite often letters at the beginning of the alphabet such as a, b, c, and d.
A variable may have one value or it may have many values in a discussion. The letters at the end of the alphabet, such as x, y, z are usually are used to represent variables. In 5x + 7, the letter x is the variable.
If x = 1, then 5x + 7 = 5 + 7 = 12
If x = 2, then 5x + 7 = 5(2) + 7 = 10 + 7 = 17
and so on for as many values of x as we desire to select.
If the expression 5x + 7 is set equal to some particular number, say -23, then the resulting equality
5x + 7 = -23
holds true for just one value of x. The value is -6, since
5(-6) + 7 = -23
In an algebraic expression, terms that contain a variable are called VARIABLE TERMS. Terms that do not contain a variable are CONSTANT TERMS. The expression 5x + 7 contains one variable term and one constant term. The variable term is 5x, while 7 is the constant term. In ax + b, ax is the variable term and b is the constant term.
A variable term often is designated by naming the variable it contains. In 5x + 7, 5x is the x-term. In ax + by, ax is the x-term, while by is the y-term.
question 1. What is Solving a Linear Equation?
Solution: Solving an equation means to find a value of the variable which satisfies the equation.
question 2. How do we solve the equation?
Solution: Stepwise RULES FOR SOLVING AN EQUATION
- Same quantity can be added to both sides of an equation without changing the equality;
- Same quantity can be subtracted from both sides of an equation without changing the equality;
- Both sides of an equation may be multiplied by a same non-zero number without changing the equality;
- Both sides of an equation may be divided by a same non-zero number without changing the equality.
The three components of an equation
Every equation has a Left hand side, the equality sign ‘=’ and the Right hand side. the three components in the equation x + 1 = 2 are :
Linear Equation |
||
L.H.S. |
Equality |
R.H.S. |
x + 1 |
= |
2 |
L.H.S = Left Hand Side, R.H.S = Right Hand Side
CBSE NCERT Solutions for Class 8 Maths
class 8 maths NCERT solutions Chapter 1: Rational Numbers
class 8 maths NCERT solutions Chapter 2: Linear Equations in One Variable
class 8 maths NCERT solutions Chapter 3: Understanding Quadrilaterals
class 8 maths NCERT solutions Chapter 4: Practical Geometry
class 8 maths NCERT solutions Chapter 5: Data Handling
class 8 maths NCERT solutions Chapter 6: Square and Square Roots
class 8 maths NCERT solutions Chapter 7: Cube and Cube Roots
class 8 maths NCERT solutions Chapter 8: Comparing Quantities
NCERT Class 8 Maths solution Chapter 9: Algebraic Expressions and Identities
class 8 maths NCERT solutions Chapter 10: Visualizing Solid Shapes
class 8 maths NCERT solutions Chapter 11: Mensuration
class 8 maths NCERT solutions Chapter 12: Exponents and Powers
class 8 maths NCERT solutions Chapter 13: Direct and Inverse Proportions
class 8 maths NCERT solutions Chapter 14: Factorization
class 8 maths NCERT solutions Chapter 15: Introduction to Graphs
class 8 maths NCERT solutions Chapter 16: Playing with Numbers
Notes,worksheet and solved question for Maths class 8
- class 8 maths notes on chapter Liner equation in one variable
- class 8 maths notes on chapter algebric expression
- class 8 maths notes on chapter Mensuration
- class 8 maths notes on chapter Square and square roots
- class 8 maths notes on chapter statistice
- class 8 maths notes on chapter practical Geometry
- class 8 maths notes on chapter commericial maths
- class 8 maths notes on chapter solid shape
- class 8 maths notes on chapter quadrilaterals
- class 8 maths notes on chapter exponents
- class 8 maths notes on chapter factorisation
- class 8 maths notes on chapter inverse proporation
- class 8 maths notes on chapter cube and cube roots
Check your marks in a chapter which you have complited in school from Physics Wallah chapter wise online test just click on the link given below
- Linear equations
- Constants and variables
- Solution/Root of an equation
- linear equations examples
- Solution Requiring more than one operation
- Equations with literal coefficients
- Removing signs of grouping:
- Equations containing fractions
- Solved questions
- Exercise 1
- Exercise 2 (Fill in the blanks)
- Exercise 3 (True and False)
- Exercise 4
- Exercise 5
- Exercise 6