1/2-3m/4 +7=4m- 9- m/28
I don't like fractions, so multiply each term by 28 , the LCD
14 - 21m + 196 = 112m - 252 - m
-132m = -462
m = 462/132 = 7/2
To solve this equation, we need to simplify and combine like terms on both sides of the equation. Let's break it down step by step:
1/2 - (3m/4) + 7 = 4m - 9 - (m/28)
First, let's simplify the fractions on both sides:
For the left side:
1/2 - (3m/4) can be written as (2/2)*(1/2) - (3m/4) = 2/4 - (3m/4) = (2 - 3m)/4
For the right side:
-m/28 can be combined with 4m: -m/28 is the same as (-1/28)*m, so we can write 4m - m/28 as (4 - 1/28)*m
Now, let's substitute the simplified fractions back into the equation:
(2 - 3m)/4 + 7 = (4 - 1/28)*m - 9
Next, we need to remove the denominators to simplify further. To do this, we can multiply the entire equation by the least common multiple (LCM) of the denominators, which is 4 * 28 = 112:
112[(2 - 3m)/4] + 112(7) = 112[(4 - 1/28)*m - 9]
Simplifying further:
28(2 - 3m) + 784 = 112(4 - 1/28)m - 1008
Now we can distribute and simplify:
56 - 84m + 784 = 448m - 112/28m - 1008
Combining like terms:
-84m - 448m = -112/28m - 784 - 1008 - 56
-532m = -112/28m - 1848
To get rid of fractions, we can multiply both sides by 28:
-532m(28) = (-112/28m - 1848)(28)
-14936m = -112 - 51696m
Now, let's isolate the variable m by grouping terms with m on one side:
-14936m + 51696m = -112
36760m = -112
Finally, solve for m by dividing both sides by 36760:
m = -112 / 36760
So the solution to the equation is m = -0.003048787.
1/2 - 3m/4 + 7 = 4m -9 - m/28
Let's get all of the m's on one side and all of the constants on the other.
1/2 + 7 + 9 =4m - m/28 + 3m/4
1/2 + 14/2+18/2 = 28(4m)/28 - m/28 +21m/28
33/2 =
combine the m terms and then solve for m by cross multiplying.