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Reducing Linear Equations into Simpler Form Video Lecture - Advance Learner
FAQs on Reducing Linear Equations into Simpler Form
| 1. What is the process of reducing linear equations into a simpler form? |  |
Ans. The process of reducing linear equations into a simpler form involves manipulating the equations using various algebraic operations, such as combining like terms, simplifying fractions, and isolating the variable on one side of the equation.
| 2. How can I combine like terms in a linear equation? | |
Ans. To combine like terms in a linear equation, you need to identify terms that have the same variables and exponents. Then, you can add or subtract the coefficients of these terms while keeping the variables and exponents unchanged.
| 3. What is the purpose of simplifying fractions in linear equations? | |
Ans. Simplifying fractions in linear equations helps to make the equations easier to work with and understand. It involves reducing the fractions to their simplest form by dividing the numerator and denominator by their greatest common divisor.
| 4. How do I isolate a variable in a linear equation? | |
Ans. To isolate a variable in a linear equation, you need to perform algebraic operations to move all other terms away from the variable, leaving it on one side of the equation. This typically involves using inverse operations, such as addition and subtraction, or multiplication and division.
| 5. Can reducing linear equations into a simpler form help in solving real-life problems? | |
Ans. Yes, reducing linear equations into a simpler form is a crucial step in solving real-life problems. By simplifying the equations, you can easily identify the relationships between variables, make calculations more manageable, and find solutions that accurately represent the given situation.
Text Transcript from Video
good morning children now we know how to
solve a linear equation but you know if
the equation is not in linear form we
can also reduce a given equation to
linear form and then solve it so let us
see here we have equation Z plus 15
divided by Z is equal to 3 by 4 now is
this a linear equation
no why if you see the expression on left
hand side that is Z plus 15 by Z is not
a linear equation but you know we can
reduce this equation to the linear form
let us see now let's try to reduce it to
the linear form z plus 15 by z is equal
to 3 by 4 first we multiply both the
sides by Z you may ask why we need to do
that this is because if we multiply put
the elitists and the RHS by Z then we'll
this can be simplified as Z in the
denominator would go off so let's do it
Z multiplied by Z plus 15 divided by Z
is equal to said x 3 by 4 let's simplify
this so desert said gets cancelled and
what are we left with we are left with Z
plus 15 is equal to 3 said by 4 or you
can say 3 by 4 z it's the same thing
next we do the cross multiplication to
simplify this and what do we do then
this here we can say the denominator is
1 and we'll do the cross multiplication
so here the LHS would be multiplied by 4
which was the divisor here and 1 which
is the divisor here
would become the multiplicand here so we
would get on the RHS 3z x 1 so 4 x z
plus 15 is equal to 3 z x 1 if you
notice we have put brackets here which
means 4 needs to be multiplied by both Z
and also 15 so let's do it we get 4 Z
plus 4 multiplied by 15 becomes 60 equal
to 3z next if you see this equation is
in linear form why because Z has only
the power which is equal to 1 now let's
solve it because we already now know how
to solve a linear equation here we have
4 Z plus 60 is equal to 3z again what we
should do subtract 3 set from both sides
why we are just following that to
simplify we should bring the variable on
one side so if we subtract 3 set from
both the sides what do we get for Z plus
60 minus 3 Z is equal to 3 Z minus 3 Z 4
Z minus 3 Z becomes Z and plus 60 we
bring it down and on the RHS what do you
see 3 said minus 3 Z equal to 0 next
what do we do we subtract 60 from both
the sides so that Z is there on the left
hand side alone with no other constant
on the side so Z equal to minus 60 how Z
plus 60 - 60 becomes Z as 60 - 60 cancel
each other and when we subtract 60 from
0
get zero minus 60 which is equal to
minus 60 on the RHS so here we see we
get the solution which is Z equal to
minus 60 again we will check if we got
the right answer or not so putting the
value of Z in the given equation the
equation is Z plus 15 by Z is equal to 3
by 4
let's put Z equal to minus 60 so putting
the value what do we get Z replaced by
minus 16 plus 15 bring it down
divided by Z so divided by minus 60 is
equal to 3 by 4 solving it what do we
get minus 60 plus 15 becomes minus 45
and minus 60 asses on the LHS on the RHS
we already have 3 by 4
simplifying this further - - gets
cancelled and 45 by 60 can also be
reduced so here we get 15 threes are 45
and 15 for a 60 so you see 3 by 4 is
equal to 3 by 4 so LHS equal to RHS and
we got the solution so now you know how
to reduce a given equation to the linear
form that's all for now bye bye children
solve a linear equation but you know if
the equation is not in linear form we
can also reduce a given equation to
linear form and then solve it so let us
see here we have equation Z plus 15
divided by Z is equal to 3 by 4 now is
this a linear equation
no why if you see the expression on left
hand side that is Z plus 15 by Z is not
a linear equation but you know we can
reduce this equation to the linear form
let us see now let's try to reduce it to
the linear form z plus 15 by z is equal
to 3 by 4 first we multiply both the
sides by Z you may ask why we need to do
that this is because if we multiply put
the elitists and the RHS by Z then we'll
this can be simplified as Z in the
denominator would go off so let's do it
Z multiplied by Z plus 15 divided by Z
is equal to said x 3 by 4 let's simplify
this so desert said gets cancelled and
what are we left with we are left with Z
plus 15 is equal to 3 said by 4 or you
can say 3 by 4 z it's the same thing
next we do the cross multiplication to
simplify this and what do we do then
this here we can say the denominator is
1 and we'll do the cross multiplication
so here the LHS would be multiplied by 4
which was the divisor here and 1 which
is the divisor here
would become the multiplicand here so we
would get on the RHS 3z x 1 so 4 x z
plus 15 is equal to 3 z x 1 if you
notice we have put brackets here which
means 4 needs to be multiplied by both Z
and also 15 so let's do it we get 4 Z
plus 4 multiplied by 15 becomes 60 equal
to 3z next if you see this equation is
in linear form why because Z has only
the power which is equal to 1 now let's
solve it because we already now know how
to solve a linear equation here we have
4 Z plus 60 is equal to 3z again what we
should do subtract 3 set from both sides
why we are just following that to
simplify we should bring the variable on
one side so if we subtract 3 set from
both the sides what do we get for Z plus
60 minus 3 Z is equal to 3 Z minus 3 Z 4
Z minus 3 Z becomes Z and plus 60 we
bring it down and on the RHS what do you
see 3 said minus 3 Z equal to 0 next
what do we do we subtract 60 from both
the sides so that Z is there on the left
hand side alone with no other constant
on the side so Z equal to minus 60 how Z
plus 60 - 60 becomes Z as 60 - 60 cancel
each other and when we subtract 60 from
0
get zero minus 60 which is equal to
minus 60 on the RHS so here we see we
get the solution which is Z equal to
minus 60 again we will check if we got
the right answer or not so putting the
value of Z in the given equation the
equation is Z plus 15 by Z is equal to 3
by 4
let's put Z equal to minus 60 so putting
the value what do we get Z replaced by
minus 16 plus 15 bring it down
divided by Z so divided by minus 60 is
equal to 3 by 4 solving it what do we
get minus 60 plus 15 becomes minus 45
and minus 60 asses on the LHS on the RHS
we already have 3 by 4
simplifying this further - - gets
cancelled and 45 by 60 can also be
reduced so here we get 15 threes are 45
and 15 for a 60 so you see 3 by 4 is
equal to 3 by 4 so LHS equal to RHS and
we got the solution so now you know how
to reduce a given equation to the linear
form that's all for now bye bye children
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Apr 18, 2026 Last updated
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