Page 101 - Maths Skills - 8

Linear Equations in One Variable 99

INTRODUCTION
You are now well-versed with algebraic expressions and their operations. Any algebraic expression becomes an
equation when it contains an ‘=’ sign. In other words, an equation is a statement of equality involving one or more
unknown measures or variables.

For example, 2x + 3 = 9, 2x + 3x – 1 = 0 and 4x + 5y = 20 are equations.
2
There are different types of equations like linear equation, quadratic equation etc. In this chapter you shall learn
about linear equations in one variable.

EQUATION
“A statement of equality involving an unknown quantity (variable) is called an equation.”

Linear Equation
An equation involving only linear polynomials is called a linear equation.
Or
An equation in which the highest power of the variable is 1 is called a linear equation.
Some examples of linear equations in one variable are as follows.

(i) x – 5 = 8 – 4x (ii) 1 x 3 (iii) 3(y – 4) = 6 (iv) 3 (a 3) 1 a
42x
4 5 5 3
RULES FOR SOLVING A LINEAR EQUATION

I. Same number can be added to both the sides of the equation without affecting the equality.
II. Same number can be subtracted from both the sides of the equation without affecting the equality.
III. Both sides of the equation can be multiplied by the same number ‘m’ (m ≠ 0) without affecting the equality.
IV. Both sides of the equation can be divided by the same number ‘m’ (m ≠ 0) without affecting the equality.

With the help of above rules, we can solve the given linear equation by using the following methods.

(i) Solving Linear Equations using Transposition Method
In the case where an equation consists of variable terms and numbers on both sides of equality, the method of
solution involves transposition or shifting of variable terms on one side and numerals on the other.
Step 1: Identify the variable terms and the numerals.
Step 2: Simplify the LHS and the RHS.
Step 3: Transpose variable terms to the LHS and numerals to Fact-o-meter
the RHS. � The variable terms are always
Step 4: Simplify the transposed LHS and RHS and reduce each transposed to the LHS and
side to a single term. the numerals to the RHS.
Step 5: Divide both the sides by the coefficient of the variable � Always remember to change
the sign, while transposing
on the LHS. from one side to the other.

(ii) Solving Linear Equations by Cross-Multiplication Method

Let there be an equation in the form px q l
rx t m
First convert equation to linear form by the method of cross-multiplication.
px q l

rx t m mpx ( q ) lrx ( t)
Now find the solution by transposition.