Question

Please dont answer if you are not 100% sure.

Make sure you answer both parts and be detailed in your explanation.

a) The equation 2x + 8 = 2(x+4) works for all values of x. Explain how you know.

b) The equation 3x +7 = 3(x+7) works for no values of x. Explain how you know.

Answer 1

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.

----------------------------------------------------------------------------------------------------------------

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.

----------------------------------------------------------------------------------------------------------------

I hope this is helpful :) Good luck