Question

Look at these three equations.



1.
6
(
x
−
2
)
=
6
x
−
3

2.
2
(
x
−
3
)
=
2
x
−
6

3.
3
(
x
−
2
)
=
x
−
6



Which of the equations has no solution?




only equation 1


only equation 3


only equations 1 and 3


equations 1, 2, and 3

Answer 1

Only equation 1.

Work:
1) 6(x − 2) = 6x − 3 → 6x − 12 = 6x − 3 → −12 = −3 (contradiction), so no solution.
2) 2(x − 3) = 2x − 6 → 2x − 6 = 2x − 6 (true for all x).
3) 3(x − 2) = x − 6 → 3x − 6 = x − 6 → 2x = 0 → x = 0.