Question 652201
{{{2(x+3)+3x=-3(x-2)+8x}}} Start with the given equation.



{{{2x+6+3x=-3x+6+8x}}} Distribute.



{{{5x+6=-3x+6+8x}}} Combine like terms on the left side.



{{{5x+6=5x+6}}} Combine like terms on the right side.



{{{5x=5x+6-6}}} Subtract {{{6}}} from both sides.



{{{5x-5x=6-6}}} Subtract {{{5x}}} from both sides.



{{{0x=6-6}}} Combine like terms on the left side.



{{{0x=0}}} Combine like terms on the right side.



{{{0=0}}} Simplify.



Since this equation is <font size=4><b>always</b></font> true for any x value, this means x can equal any number. So there are an infinite number of solutions.



So the answer is


1) Conditional
<font color="red">2) Identity</font>
3) Contradiction