x = 1350 + (25x)/100
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We are given an equation x = 1350 + (25x)/100
We have to solve the equation to find the value of 'x'
Now, first of all
[tex]\frac{25x}{100}[/tex] can be simplified and written as [tex]\frac{x}{4}[/tex]
So, the equation can be rewritten as
[tex]x=1350+\frac{x}{4}[/tex]
We will multiply the whole equation by 4
[tex]4=5400+x[/tex]
[tex]x=4-5400[/tex]
[tex]x=-5396[/tex]
The value of 'x' will be -5396.
Given expression:-
[tex]x=\frac{1350+25x}{100}[/tex]
We have to simplify the expression for x,
Breaking the fraction,
[tex]x=\frac{1350}{100}+\frac{25x}{100}[/tex]
Find the greatest common factor of the numerator and denominator:
[tex]x=\frac{(27\times 50)}{(2\times 50)} +\frac{25x}{100}[/tex]
[tex]x=\frac{27}{2}+\frac{1}{4} x[/tex]
Subtract both sides by [tex]\frac{1}{4} x[/tex] from both sides,
[tex]=>x-\frac{1}{4}x=\frac{27}{2} +\frac{1}{4} x-\frac{1}{4} x[/tex]
[tex]=>\frac{4}{4}+\frac{-1}{4}x=\frac{27}{2} +\frac{1}{4} x-\frac{1}{4} x[/tex]
[tex]=>\frac{3}{4}x=\frac{1}{4} x+ \frac{-1}{4} x+\frac{27}{2}[/tex]
By simplifying it we get,
[tex]=>\frac{3}{4}x=\frac{1-1}{4}x+\frac{27}{2}[/tex]
[tex]=> \frac{3}{4}x=\frac{0}{4}x+\frac{27}{2}[/tex]
[tex]=> \frac{3}{4}x=\frac{27}{2}[/tex]
Multiply both sides by an inverse fraction [tex]\frac{4}{3}[/tex]
[tex]=> \frac{3}{4}x\times\frac{4}{3}=\frac{27}{2}\times \frac{4}{3}[/tex]
[tex]=>x=\frac{27}{2} \times \frac{4}{3}[/tex]
[tex]=>x=18[/tex]
Hence, the value of x is 18.