Verified Answer :

\(0.2(x + 1) + 0.5x = -0.3(x - 4)\) 

\(0.2x+0.2+0.5x=-0.3x+1.2\) 

\(0.7x+0.2=-0.3x+1.2\) 

\(0.7x=-0.3x+1.2-0.2\) 

\(0.7x=-0.3x+1\) 

\(0.7x+0.3x=1\) 

\(x=1\)

Answer:  The required value of x is 1.

Step-by-step explanation:  We are given to solve the value of x in the following equation :

\(0.2(x+1)+0.5x=-0.3(x-4)~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\)

To find the value of x in the above equation, we must solve the equation (i) as follows :

\(0.2(x+1)+0.5x=-0.3(x-4)\\\\\Rightarrow 0.2x+0.2+0.5x=-0.3x+1.2\\\\\Rightarrow 0.7x+0.2=-0.3x+1.2\\\\\Rightarrow 0.7x+0.3x=1.2-0.2\\\\\Rightarrow x=1.\)

Thus, the required value of x is 1.