Solve for variable 2/3 + 4m/3 = 34/3

M=8 2
+
3

4m
=
3

34


2 Join the denominators.
2
+
4
m
3
=
3
4
3
3

2+4m
=
3

34


3 Factor out the common term
2
2.
2
(
1
+
2
m
)
3
=
3
4
3
3

2(1+2m)
=
3

34


4 Multiply both sides by
3
3.
2
(
1
+
2
m
)
=
3
4
3
×
3
2(1+2m)=
3

34
×3

5 Simplify
3
4
3
×
3
3

34
×3 to
1
0
2
3
3

102
.
2
(
1
+
2
m
)
=
1
0
2
3
2(1+2m)=
3

102


6 Simplify
1
0
2
3
3

102
to
3
4
34.
2
(
1
+
2
m
)
=
3
4
2(1+2m)=34

7 Divide both sides by
2
2.
1
+
2
m
=
3
4
2
1+2m=
2

34


8 Simplify
3
4
2
2

34
to
1
7
17.
1
+
2
m
=
1
7
1+2m=17

9 Subtract
1
1 from both sides.
2
m
=
1
7
−
1
2m=17−1

10 Simplify
1
7
−
1
17−1 to
1
6
16.
2
m
=
1
6
2m=16

11 Divide both sides by
2
2.
m
=
1
6
2
m=
2

16


12 Simplify
1
6
2
2

16
to
8
8.
M=8