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

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

Step2: Simplify both sides

Left: $0.6x + 0.2 - 0.1x = 0.5x + 0.2$
Right: $0.5x + 1 - 0.8 = 0.5x + 0.2$

Step3: Compare both sides

$0.5x + 0.2 = 0.5x + 0.2$
Subtract $0.5x + 0.2$ from both sides: $0=0$

Answer:

infinitely many solutions