Question

Look at the equation.



2
5
y
−
3
2
=
−
8
(
1
4
−
1
20
y
)



If the equation is solved for
y
, which statement is true?


The solution to the equation is
y
=
−
20
21
.


The solution to the equation is
y
=
−
5
3
.


The equation has no solution.


The equation has infinitely many solutions.

Answer 1

Interpreting the equation as (2/5)y − 3/2 = −8(1/4 − (1/20)y):

Right side: −8(1/4 − 1/20 y) = −8(1/4) + 8(1/20)y = −2 + (2/5)y.

So (2/5)y − 3/2 = (2/5)y − 2. Subtract (2/5)y from both sides to get −3/2 = −2, a contradiction.

Therefore the equation has no solution.