Question

3(x-2)+2x=1/2(10x-12)

Answer 1

this equation is always true

Explanation:

3(x-2)+2x=1/2(10x-12)

3x - 6 + 2x = 5x - 6

5x - 6 = 5x -6

5x - 5x = 6 - 6

0 = 0

this equation is always true

Answer 2

Infinitely many solutions

Explanation:

`\sf 3(x - 2) + 2x = (1)/(2)*(10x - 12)\\\\ 3x - 3*2 + 2x = (1)/(2)*10x - (1)/(2)*12 \ [\bf distributive \ property]\\\\ 3x - 6 + 2x = 5x - 6`

Combine like terms,

3x + 2x - 6 = 5x - 6

5x - 6 = 5x - 6

There are infinitely many solutions for this equation.