Question

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

Solve each:

1) 6(x−2)=6x−3 → 6x−12=6x−3 → −12=−3 (contradiction) ⇒ no solution.

2) 2(x−3)=2x−6 → 2x−6=2x−6 ⇒ identity ⇒ all real numbers are solutions.

3) 3(x−2)=x−6 → 3x−6=x−6 → 2x=0 → x=0 (one solution).

Answer: only equation 1.