Answer: m = -7; r = 4; y = -6
Step-by-step explanation:
1/9 (2m - 16) = 1/3 (2m + 4)
2/9m - 16/9 = 2/3m + 4/3
Bring like terms together
Subtract 2/3m from both sides
2/9m - 2/3m - 16/9 = 4/3
Add 16/9 to both sides
2/9m - 2/3m = 4/3 + 16/9
Find the LCM (Least Common Multiple) of 3m and 9m
3m = 3m, 6m, 9m, 12m...
9m = 9m, 18m..
LCM = 9m
Multiply 3 to the denominator and nominator of 2/3m so the denominator can be 9.
2/3 × 3/3 = 6/9
Also find the LCM (Least Common Multiple) of 3 and 9
3 = 3, 6, 9, 12...
9 = 9, 18..
LCM = 9
Multiply 3 to the denominator and nominator of 4/3 so the denominator can be 9.
4/3 × 3/3 = 12/9
Now the equation looks like this..
2/9m - 6/9m = 12/9 + 16/9
Combine like terms
-4/9m = 28/9
Multiply -9/4 in both sides
m = -7
-4(r + 2) = 4(2 - 2r)
Distribute in both sides
-4r - 8 = 8 - 8r
Add 8r to both sides
-4r + 8r - 8 = 8
Add 8 to both sides
-4r + 8r = 8 + 8
Combine like terms
4r = 16
r = 4
12 (5 + 2y) = 4y - (6 - 9y)
The equation is basically:
12 (5 + 2y) = 4y - 6 + 9y
So distribute 12..
60 + 24y = 4y - 6 + 9y
60 + 24y = 13y - 6
Subtract 13y from both sides
60 + 11y = -6
Subtract 60 from both sides
11y = -66
Divide both sides by 11
y = -6
Hope this helped!
