Question

Solve for x: 3/5x+1=2/5-3x​

Answer 1

According to the question it is given that,

$\frac{3}{5}x+1=\frac{2}{5} -3x$

To simplify the given expression for x,

Add $3x$ on both sides we get,

$=>\frac{3}{5} x+1+3x=\frac{2}{5} -3x+3x$

$=>\frac{3}{5} x+3x+1=\frac{2}{5} -3x+3x$

By converting the integer into a fraction,

$=>\frac{3}{5} x+\frac{15}{5}x +1=\frac{2}{5} -3x+3x$

$=>\frac{3+15}{5}x+1 =\frac{2}{5} -3x+3x$

By simplifying it, we get

$=>\frac{18}{5}x+1=-3x+3x+\frac{2}{5}\\=>\frac{18}{5}x+1= \frac{2}{5}$

Subtract both sides by 1 from both sides,

$=>\frac{18}{5}x+1-1=\frac{2}{5} -1\\=>\frac{18}{5}x=\frac{2}{5} -1$

Again convert the integer into a fraction,

$=>\frac{18}{5}x=\frac{2}{5}+\frac{-5}{5}\\=>\frac{18}{5}x= \frac{2-5}{5}\\=>\frac{18}{5} x=\frac{-3}{5}$

Multiply both sides by an inverse fraction $\frac{5}{18}:$

$=>\frac{18}{5} \times\frac{5}{18}x =\frac{-3}{5}\times\frac{5}{18} \\=>x=\frac{-3}{5}\times\frac{5}{18}\\x=\frac{-1}{6}$

Hence, the value of x is $\frac{-1}{6}$

Answer 2

Given equation,

$\frac{3}{5} x+1=\frac{2}{5}-3x$

To solve this equation all the $x$ variables should be in LHS and all the constant terms should be in RHS.

$\frac{3}{5} x+3x=\frac{2}{5} -1\\\frac{3x+15x}{5} =\frac{2-5}{5}\\18x=-3\\x=\frac{-3}{18} \\x=\frac{-1}{6}$

Therefore the value of $x$ is $\frac{-1}{6}$