Question

divide both sides:divide both sides by what?
\\(\boldsymbol{\frac{2}{5}x = 4 + \frac{3}{5}x}\\)

Explanation:

Step1: Identify target coefficient

The goal is to isolate $x$, starting from the equation $\frac{2}{5}x = 4 + \frac{3}{5}x$. First, we need to get all $x$ terms on one side.

Step2: Subtract $\frac{3}{5}x$ from both sides

$\frac{2}{5}x - \frac{3}{5}x = 4 + \frac{3}{5}x - \frac{3}{5}x$
$\frac{2-3}{5}x = 4$
$-\frac{1}{5}x = 4$

Step3: Divide to solve for $x$

To isolate $x$, divide both sides by the coefficient of $x$, which is $-\frac{1}{5}$.
$\frac{-\frac{1}{5}x}{-\frac{1}{5}} = \frac{4}{-\frac{1}{5}}$

Answer:

$-\frac{1}{5}$

(Note: If referring to the original left-hand side coefficient before rearranging, the value to divide both sides by to isolate $x$ from $\frac{2}{5}x$ is $\frac{2}{5}$, but after collecting like terms, the coefficient to divide by is $-\frac{1}{5}$. The key value to divide by to solve for $x$ in the simplified equation is $-\frac{1}{5}$.)