Answer:
(c) III
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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I.
2x -6 -6x = 2 -4x . . . . eliminate parentheses
-4x -6 = -4x +2 . . . . no solutions (no value of x makes this true)
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II.
x +2 = 15x +10 +2x . . . . eliminate parentheses
x +2 = 17x +10 . . . . one solution (x=-1/2)
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III.
4 +6x = 6x +4 . . . . eliminate parentheses
6x +4 = 6x +4 . . . . infinite solutions
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IV.
6x +24 = 2x -4 . . . . eliminate parentheses; one solution (x=-7)