how do I solve 3(7-x) = 6(x-1)?

Question

I have a general idea how to do it:
I would use the distibutive property to combine like terms:

21-3x=6x-6 right?

then i would have to combine like terms again:
6x-3x=21-(-6x) right?

i would then have 3x=15 with x being 3?

Am i close? I get so confused on where to put the numbers when i am combining the like terms and when to change the symbols.

Answer 1

3(7 - x) = 6(x - 1)

21 - 3x = 6x - 6

21 - 3x + 3x = 6x - 6 + 3x

21 = 9x - 6

21 + 6 = 9x - 6 + 6

27 = 9x

27/9 = 9x / 9

3 = x

The answer is s = 3

Insert the x value into the equation

- - - - - - - - - - - - - - - - - - - - - - -

Check

3(7 - x) = 6(x - 1)

3 (7 - 3) = 6(3 - 1)

3(4) = 6(3)

12 = 12

- - - - - -s-

Answer 2

Multiply out the brackets both sides

==> 21 - 3x = 6x - 6

Add 3x to both sides

==> 21 - 3x + 3x = 6x - 6 + 3x
==> 21 = 9x -6

Add 6 to both sides

==> 27 = 9x

Divide both sides by 9

==> 27/9 = 9x/9

==> 3 = x

Rearrange to get in the usual form

==> x = 3

Answer 3

the others have given you the answer but really havent explained it. when you combine like terms, you should write it down instead of doing it in your head. for example in this equation,
21-3x=6x-6, you have a 3x on the left side with a "-" sign in front of it. in order to cancel that out, you would need to add 3x to the left. you must also add 3x to the right side. underneath the -3x you should write +3x. underneath the 6x you should also write +3x. this will cancel out the 'x' terms on the left and leave you with 21=9x-6. you would do the same with the whole numbers. you have a -6 on the right, so underneath add a +6 on both sides of the equation. you now have 27=9x, and x =3.
im positive this will help you from getting confused.

Answer 4

3(7-X) = 6(X-1) Multiply into the brackets
21 - 3x = 6x - 6 Bring x's into left and numbers to the right.

-3x - 6x = -6 - 21 Solve this you will get
-9x = -27 you can cancel out the minus
9x = 27 bring the 9 to the other side

x = 27 / 9 = 3

Hope this helps

Answer 5

3(7-x)=6(x-1)
distributive property:
21-3x=6x-6
transpose:
21+6=6x+3x
combine like terms:
27=9x
divide by the numerical coefficient, both sides:
27/9=9x/9
resulting quotient:
3=x
recheck:
21-3(3)=6(3)-6
21-9=18-6
12=12

Answer 6

Personally I find it easier to do it as below.

3(7-x) = 6(x-1)

Expand the terms as you did.

21-3x=6x-6

Then i would move the numbers to one side and the x's to the other (Don't forget that positive numbers change to negative and vice versa when moving them across the = sign) i.e.

(21+6)-3x = 6x
27=6x+3x
27=9x

Then move the 9 across the equals, changing the multiply to a divide.

27/9=x
x=3

In short, change the symbols when you move the number across the equals. Try and get all the numbers to one side and the x's to the other, should be simpler that way. Hope that helps.

Answer 7

Well, It's pretty simple:

3(7-X)=6(X-1)
21-3X=6X-6
-3X-6X=-6-21
-9X=-27
X=3

And anyawy, whenever you are not sure if you were right, just put the number you found instead of the X and see if it's making any sense

Answer 8

The easiest way to do is to get rid of the x's first. Thus, you can multiply the eq1 by 6, so it becomes 6x + 24y = 222. Now use this to subtract eq2. 6x + 24y = 222 - 6x + 3y = 75 --> 6x-6x = 0, 24y - 3y = 21y, and 222 - 75 = 147. Now you have 21y = 147. y then equals 7. Plug y = 7 back to eq1, you have x + 4(7) = 37. So, x + 28 = 37. x = 37-28, which is 9. Here is the final ans: x = 9, and y = 7. Good luck!!

Answer 9

21-3x=6x-6
take like terms one side.
-3x-6x=-6-21
=>-9x=-27
=>x=3

Answer 10

3(7-x)=6(x-1)
21-3x= 6x -6
21+6= 6x+3x
27= 9x
x= 27/9
x=3