Page 112 - Maths Skills - 8

110 Maths

MIND MAP

Linear Equations in One Variable

“An equation is a sentence that has two equal mathematical expressions
e.g. 4x + 9 = 3x + 10 (one variable)”

Type

Linear Equation Non-Linear Equation
An equation involving one variable An equation involving one variable with
with single power i.e. x + 11 = 0 more than single power i.e. x + 9 = 0
2

Solution
A number which substituted for the
variable in the equation makes both
the sides equal is called a solution.

Methods for Solutions Verification
Any linear equation in one variable can After finding the solution of equation,
be solved using following methods. then for verification put the value of that
1. Cross-multiplication method variable in both sides of given equation
2. Transposition method if L.H.S. = R.H.S.
then, it is verified

Rememberable Points

� Consecutive numbers are taken as x + 1, x + 2, x + 3 ............
� Consecutive even numbers are taken as x, x + 2, x + 4 ............
� Consecutive odd numbers are taken as x, x + 2, x + 4 ............
� Consecutive multiple of 4 are taken as x, x + 4, x + 8 ............
� Down stream speed must be taken with ‘+’ sign i.e. x + y where x = speed of boat, y = speed of stream
� Upsteam speed must be taken with ‘–’ sign i.e. x – y
� Distance = speed × Time