Answer:
   (c)  III
Step-by-step explanation:
If you simplify the equations and the left side is identical to the right side, then there are an infinite number of solutions: the equation is true for all values of x.
Another way to simplify the equation is to subtract the right side from both sides. If that simplifies to 0 = 0, then there are an infinite number of solutions.
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<h3>I. </h3>
   2x -6 -6x = 2 -4x . . . . eliminate parentheses
   -4x -6 = -4x +2 . . . . no solutions (no value of x makes this true)
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<h3>II.</h3>
   x +2 = 15x +10 +2x . . . . eliminate parentheses
   x +2 = 17x +10 . . . . one solution (x=-1/2)
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<h3>III.</h3>
   4 +6x = 6x +4 . . . . eliminate parentheses
   6x +4 = 6x +4 . . . . infinite solutions
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<h3>IV.</h3>
   6x +24 = 2x -4 . . . . eliminate parentheses; one solution (x=-7)