Question

Which of the following equations has the solution x = all real numbers?

O 4(3-x) + 7x = 4x + 12 + 2x
O 4(4-x) + 6x = x + 16 - 4x
O 3(4-x) + 6x = 4x + 12 - x
O 4(3-c) + 6x = 3x + 8x

Answer 1

Answer: 3(4-x) + 6x = 4x + 12 - x

Explanation:

For the solution to be all real numbers, the left hand has to be identical to the right hand side.

1)
`4(3-x)+7x=12-4x+7x=12+3x`, so wrong.

2)
`4(4-x)+6x=16-4x+6x=16+2x`, so wrong.

3)
`3(4-x)+6x=12-3x+6x=12+3x=4x+12-x`, so correct.

4) Wrong variable, so eliminate immediately.