Question 921010
If you solve an equation and get to an absolute truth (a statement not involving variables that is true), you have infinitely many solutions.

Example:

If you solve this you get:
{{{x + 5 = x + 5}}}
{{{5 = 5 }}} which is an absolute truth (a statement not involving variables that is true)

so, solve your equation for {{{m}}}:

{{{mx + 3(mx -12) + 14 = 11(x -2) + 5x}}}

{{{mx + 3mx -36 + 14 = 11x -22 + 5x}}}


{{{mx + 3mx - cross(22) = 16x –cross(22)}}}

{{{(m + 3m)cross(x)  = 16cross(x) }}}

{{{4m  = 16 }}}

{{{m  = 16/4 }}}

{{{m  = 4 }}}


check if we get an absolute truth (a statement not involving variables that is true) if we plug in {{{m  = 4 }}}


{{{4x + 3(4x -12) + 14 = 11(x-2) + 5x}}}

{{{4x + 12x -36 + 14 = 11x -22 + 5x}}}

{{{16x -22 = 16x – 22 }}}

{{{16x  = 16x  }}}

{{{16x-16x =0 }}}

{{{0 =0 }}}

line {{{4x + 3(4x-12)}}}

{{{ graph( 600, 600, -10,10, -10, 10, 4x + 3(4x-12) + 14 ) }}} 

line {{{ 11(x -2) + 5x}}}


{{{ graph( 600, 600, -10,10, -10, 10,  11(x -2) + 5x ) }}}

together,{{{4x + 3(4x-12)=11(x -2) + 5x}}}

{{{ graph( 600, 600, -10,10, -10, 10,16x , 16x  ) }}}

as you can see   two lines are directly on top of each other