LEARN MATH STEP BY STEP THROUGH VERY EASY PROCESS

METHOD OF SOLVING A LINEAR INEQUATION IN ONE VARIABLE

**Method of Solving a Linear Inequation in One Variable** –

**(i) Simplify both sides by removing group symbols and
collecting like terms.**

**(ii) Remove fractions (or decimals) by multiplying both
sides by an appropriate factor (L.C.M of Fractions or a power of 10 in case of
decimals.)**

**(iii) Collect all variable terms on one side and all
constants on the other side of the inequality sign. Collect like terms when
possible.**

**(iv) Make the coefficient of the variable 1.**

**(v) Choose the solution set from the replacement set.**

**Some special sets of numbers shown on number line –**

**We would like to have a glimpse on how we present sets of
numbers on number line. Some sets of numbers and their graphs are given below **

__Graphs of Subsets
of N, W, and I__

**(i) Graph of {x : - 1 < x < 5, x ϵ N} =
{1, 2, 3, 4, 5} **

**(ii)
Graph of {x : -1 < x < 4, x ϵ W} = {0, 1, 2, 3}**

**(iii) Graph of {x : x
> 2, x ϵ N} = {3, 4, 5, 6, 7, …………}**

**The dot points indicates the natural numbers contained in
the set and similarly continued dotted points above the right part of the line show that natural numbers are
continued indefinitely.**

**(iv) Graph of {x : x
< -1, x ϵ I} = {-2, -3, -4, -5, ………….}**

**The dot points show the integers contained in the set and
three dark dots above the left part of the line show the indefinite continuity
of negative integers.**

__Graphs of sets of
all real numbers between two given numbers –__

**We show the end points of the set by two red color point,
namely a hollow circle for the number not contained in the set and the blue
color both side arrow area for the number contained in the set, and the line
segment between these circles is shown by blue colored line. **

**(v) Graph of {x : - 1 ≤ x ≤ 3, x ϵ R}**

**Note that, the end points -1 and 3 are both contained in the
set.**

**(vi) Graph of {x : -
2 ≤ x < 4, x ϵ R} **

**Note that – 2 is
there in the given set while 4 is not contained in it**

__Graphs of {x :
x > a, x ϵ R} and {x : x
≥ a, x ϵ R} - __

**Such a set has one end point. The ray
to the right of this point is denoted by blue color both side arrow. If the end
point is contained in the set, then it is shown by a blue color both side arrow
line.**

**(i) Graph of {x : x ≥ 4, x ϵ R}**

**Note that the
end point 4 is continued in the given set.**

**(ii) Graph of {x : x > 3, x ϵ
R}**

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