Answer:
Step-by-step explFirst, convert each mixed number into an improper fraction:
2
5
12
=
−
3
1
4
+
k
2
+
5
12
=
−
(
3
+
1
4
)
+
k
(
12
12
×
2
)
+
5
12
=
−
(
[
4
4
×
3
]
+
1
4
)
+
k
24
12
+
5
12
=
−
(
12
4
+
1
4
)
+
k
29
12
=
−
13
4
+
k
Next, add
13
4
to each side of the equation to isolate
k
while keeping the equation balanced:
13
4
+
29
12
=
13
4
−
13
4
+
k
13
4
+
29
12
=
0
+
k
13
4
+
29
12
=
k
Then, we need to put
13
4
over a common denominator so we can add the two fractions by multiplying it by an appropriate form of
1
:
(
3
3
×
13
4
)
+
29
12
=
k
39
12
+
29
12
=
k
68
12
=
k
Now, if necessary we can convert the improper fraction back into a mixed number:
60
12
+
8
12
=
k
5
+
4
×
2
4
×
3
=
k
5
+
4
×
2
4
×
3
=
k
5
+
2
3
=
k
5
2
3
=
k
k
=
5
2
3