Pre algebra equations?

Question

what does m equal on the following equations 2/3(m-6)=3, 4/7(m+6)=2, 12m-6.5m+7= -15 , and what is the solution for this question? what is the solution of 1/2 (m-1=1/2 does anybody know the answers for the m's in all of these 4 questions

Answer 1

-----2/3(m-6)= 3

m = 10 and 1/2


----4/7 (m+6) = 2
m = - 2 and 1/ 2


-----12m - 6.5m +7 = -15
m = 4 and 6/11

-----1/2 (m - 1 = 1/2)
m = 2

Answer 2

Let's work backwards...

1/2(something) = 1/2. Hmm.....what number could "something" me if you can multiply it by 1/2, and still get 1/2? That "something" has to be 1, because anything times 1 is still anything. So since (m-1) has to be 1, so m has to be 2. That was easy.

Now, 12m - 6.5m + 7 = -15. Well 12 apples minus 6.5 apples would leave you with 5.5 apples, so 12m - 6.5m would equal 5.5m. And now you want to get all the numbers without an "m" on one side, and all the numbers with an "m" on the other side, so if you subtract 7 from both sides you get 5.5m = -22. If you show your work so far, you've got:

12m - 6.5m + 7 = -15
(12m - 6.5m) + 7 = -15
5.5m + 7 = -15
5.5m + 7 - 7 = -15 - 7
5.5m = -22

So, now divide both sides by 5.5, and you get:

m = 22/5.5

That looks ugly...lets multiply both the top and the bottom by two - since 2/2 = 1, and 1 times anything still equals anything, we can do that, and so:

m = 44/11

Hey, look....that reduces to m = 4. That looks right!

Now the first two, you need to use the distributive property to get the rid of the parenthesis:

4/7(m + 6) = 2
4/7m + 4/7*6 = 2
4/7 m + 24/7= 2

This is too messy....let's try multiplying both sides by 7:

7(4/7m + 24/7) = 2*7
4m + 24 = 14

That looks nice... subtract 24 from both sides, and:

4m = -10

so m = -10/4 = -5/2 or -2 1/2 (negative two and a half)

Can you do the first one all by yourself?

Answer 3

Question 1
2m - 12 = 9
2m = 21
m = 21 / 2

Question 2
4m + 24 = 14
4m = - 10
m = - 10/4
m = - 5/2

Question 3
5.5 m = - 22
m = - 22 / 5.5
m = - 22 / 5/2
m = - 44 / 5

Question 4
(m - 1) = 1
m = 2