Page 61 - SM inner class 8.cdr

+ 4 % 1 ¼ 3 ÷ ¾

×
Chapter8 6 ½ – Linear Equation

in One Variable

Introduction 2. If a = b then a c b c- = - for any c. This
means that we can subtract a number, c to
We are already familiar with the algebraic both sides of the equation and the
expressions and polynomials. The value of an equation will not be change.
algebraic expression depends on the values of 3. If a = b then ac = bc for any c. This means
the variables involved it. We have also learnt that we can multiply a number, c to both
about polynomial in one variable and their sides of the equation and the equation will
degrees. A polynomials in one variable whose not be change.
degree is one is called a linear polynomial in a b
4. If a = b then = for any c. This means
one variable. c c
A mathematical statement that has two that we can divide both sides of an
equation by a non-zero number, c, and the
expressions separated by an equal sign is
equation will not be change.
called an Equation. The expression on the left
side of the equal sign has the same value as the For example:
expression on the right side. 1. x - 4 = 7 Þ 7 + 4 (By transposition of 4)

The equality sign shows that the expression to Þ x - 4 + 4 = 7 + 4 (Add 4 to both sides)
the left of the sign(the left hand side or LHS) is Þ x = 11
equal to the expression to the right of the sign
2. x + 5 = 9 Þ x = -9 5
(the right hand side or RHS). An equation is a
Þ x = 4 (By transposition of 5)
statement of equality of two algebraic
expressions involving one or more unknown Þ x + 5 - 5 = 9 - 5
(Subtract 5 from both sides)
quantities, called variables. A linear equation
is an equation involving linear polynomials. Þ x + 0 = 4 Þ x = 4
For example: 3. x = 5 Þ x = 5 ´ 2
(i) 3x + 7 = 22 (ii) 4x - y = 8 2 (By cross multiplication)

(iii) 5x - 3y + 4z - 14 = 0
x =10
Re mem ber x
Þ × 2 = 5 × 2
Expression on the left hand side is known as LHS 2
and on the right hand side is known as RHS of the (Multiply 2 to both the sides)
equation. LHS and RHS are the sides of an Þ x = 10
equation.
.
024
4. 0.2x = 0.24 Þ x =
.
Rules for solving Linear equation in one 02
(By transposition of 0.2)
variable (Rules for Transposition)
.
= x = 0 12
=
1. If a = b then a + c b + c for any c. This 02x 024
.
.
means that we can add a number, c to Þ = (Divide both sides by 0.2)
.
02 02
.
both sides of the equation and the
equation will not be change. Þ x = 0.12

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Mathematics In Focus - 8