Question

identify the number of solutions for the equation: 0.2(3x + 1)-0.1x = 0.5(x + 2)-0.8. answer: no solution, one solution, infinitely many solutions

Explanation:

Step1: Expand both sides

$0.2(3x + 1)-0.1x=0.6x + 0.2-0.1x=0.5x+0.2$ and $0.5(x + 2)-0.8=0.5x+1 - 0.8=0.5x + 0.2$

Step2: Analyze the equation

The equation becomes $0.5x+0.2 = 0.5x+0.2$.
Since the left - hand side is identical to the right - hand side for all values of $x$, any real number $x$ will satisfy the equation.

Answer:

infinitely many solutions