Question

John claims the following two equations are equivalent:

−
2
(
5
y
−
3
)
=
−
10
y
−
6


John's work in determining an expression equivalent to the first expression is shown below.

−
2
(
5
y
−
3
)

=
(
−
2
⋅
5
y
)
−
(
−
2
⋅
−
3
)

=
−
10
y
−
6


Which statement explains why John's claim is incorrect?

He should have subtracted
(
−
2
⋅
3
)
resulting in the expression
−
10
y
+
6
.


He should have only multiplied
3
by
−
2
resulting in the expression
5
y
−
6
.


He should have only multiplied
5
y
by
−
2
resulting in the expression
−
10
y
−
3
.


He should have only multiplied
3
by
−
2
and subtracted
(
−
2
⋅
3
)
resulting in the expression
5
y
+
6
.

Answer 1

Correct answer: He should have subtracted (−2⋅3) resulting in the expression −10y + 6.

Explanation: −2(5y − 3) = (−2)(5y) − (−2)(3) = −10y − (−6) = −10y + 6. John mistakenly treated −2(−3) as −6 instead of +6.