Answer:
<u>No solution:.</u>
We get a no solution when the linear equality give some absurd results.
Hence, let us suppose we write the given equality as:
2x+9+3x+x=6x+10
since,
on solving this equality we get:
2x+3x+x+9=6x+10 ( on combining like terms in the left hand side of the equality)
6x+9=6x+10
6x-6x=10-9 ( on taking the variable terms to one side of the equation and constant term to other side)
0=1
which is absurd.
Hence, we get a No solution.
<u>One solution:</u>
one solution means that on solving the linear equality we get a unique value for our variable x and hence the solution is also called a unique solution.
We will write our equation as:
2x+9+3x+x=2x+17
on solving:
2x+3x+x+9=2x+17
6x+9=2x+17
6x-2x=17-9
4x=8
x=2.
Hence, we get a unique solution.
<u>Infinitely many solution:</u>
Infinite many solution means that the equation will hold true for infinitely many values of 'x' i.e we do not get a unique value.
so,
2x+9+3x+x=6x+9
2x+3x+x=6x+9
6x+9=6x+9
6x-6x=9-9
0=0
Hence, we can get infinite values or our x.
