Can you help me to do this linear equation?

Question

I can do the ones with just one fraction, but I don't know where to go on this one...

[(3m+4)/2] - [(2m-4)/3] = 30

I need to make m the subject of the equation to solve it. The back of the book says the answer should be m=44, but all I get is 33. Can you please help?

Answer 1

Sure, I can help.

(3m+4)/2 - (2m-4)/3 =30

Multiply everything by 6 to clear the fractions.

3(3m+4) - 2(2m-4)= 180

Distribute

9m+12 -4m+8= 180

Combine like terms.

5m+20= 180

Subtract 20 from both sides.

5m= 160

Divide

m= 32

The book is wrong. That happens sometimes. My calculator also solved it to be this. Are you sure you copied the problem right and/or looked at the right answer?

Answer 2

Umm, I just used a calculator and tried m=44 into the equation that you gave. It doesn't work out. It would not be the first time that the back of the book is wrong!! I worked out your problem step by step, cause 33 doesn't work either.

Multiply both sides by 6, cause personally, I hate fractions.

6[(3m+4)/2 - (2m-4)/3] = 6*30

Distribute on the left

6(3m+4)/2 - 6(2m-4)/3 = 6*30

Simplify

3(3m+4) - 2(2m-4) = 180

Distribute once again, remember to change the sign when you drop the second parenthesis

3*3m+3*4 - 2*2m+2*4 = 180

Simplify again

9m+12 - 4m+8 = 180

Collect like terms

5m+20=180

Subtract 20 from both sides

5m=160

m=32

The good news is that you were closer than the book was!

Hope that helped

Answer 3

I'm getting m = 32, the book answer sounds a little fishy....

Multiply the equation by 6 on both sides of the eqn to get rid of the fraction, your eqn now will look like this.....

3(3m+4) - 2(2m-4) = 180
9m + 12 - 4m + 8 = 180
9m - 4m + 12 + 8 = 180
5m + 20 = 180
5m = 180 - 20
5m = 160
m = 160/5 = 32

Answer 4

There are some wonderful answers on here.
Check 44, does it work?

(3(44) + 4 )/ 2 - (2(44) - 4) / 3 = 30

136 / 2 - 84 / 3 = 30

68 - 28 = 30

That actually comes out to be 40 not 30! If you copied the problem right, then the answer in the back of the book is wrong.

The solutions at the top of the page seem to be correct to me, but what would I know, I only have a degree in mathematics and hope to be a teacher next fall.

Answer 5

MULTIPLY BOTH THE SIDES BY 6

You get 3(3m+4)- 2(2m-4)=180

9m+ 12-4m+8= 180

5m=180-20=160

m=160/5=32

Answer 6

I think you combine the 3m with the 2m but the problem is i'm not sure if the (2m-4)/3 should be positive or negative because i've never done it with brackets...try turining (2m-4)/3 to -2m+4/-3 and see if you get m=44...

Answer 7

First thing is to get rid of the fractions...
18m+12-12m-8=180
6m+4=180
6m/6=184/6
m=30.6
I keep getting this...sorry.

Answer 8

I believe the correct answer is 32. But when in doubt, just substitude the numbers and see which is correct.