Answer:
a) 2x + 8 = 2(x + 4) has infinite solutions because it simplifies down to x = x. Here is the work where this equation is solved.
2x + 8 = 2(x + 4)
2x + 8 = 2(x) + 2(4)
2x + 8 = 2x +8
2x + 8 - 8 = 2x + 8 -8
2x = 2x
2x/2 = 2x/2
x = x
So, because the equation ends in x = x, you can substitute any value for x and the equation will remain true.
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b) 3x + 7 = 3(x + 7) has no solutions because it simplifies down to an untrue statement. The equation is simplified below.
3x + 7 = 3(x + 7)
3x + 7 = 3(x) + 3(7)
3x + 7 = 3x + 21
3x + 7 - 7 = 3x + 21 - 7
3x = 3x + 14
3x/3 = 3x/3 +14
x = x + 14
However, this is false. x cannot be equal to itself plus 14.
x ≠ x + 14
The simplification of this equation is untrue, so there is no solution to it.
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I hope this is helpful :) Good luck
