Linear equation w/ several occurences of the variable

crappiefisher26

New member
1. (8/3)x-3=(2/3)x+15
2.(12/5)+7=31-(3/5)x

heres the example they give me. still cant figure it out though

Solve for x.

6-(1/2)x=(3/5)+x

it says ya need to isolate the variable x. We first add (1/2)x to both sides and subtract (3/5) from both sides

then they got 6-(3/5)=x+(1/2)x

(27/5)=(3/2)x

(2/3) times (27/5)=(2/3)times(3/2)x

TchrWill

Full Member
1. (8/3)x-3=(2/3)x+15
2.(12/5)+7=31-(3/5)x

heres the example they give me. still cant figure it out though

Solve for x.

6-(1/2)x=(3/5)+x

it says ya need to isolate the variable x. We first add (1/2)x to both sides and subtract (3/5) from both sides

then they got 6-(3/5)=x+(1/2)x

(27/5)=(3/2)x

(2/3) times (27/5)=(2/3)times(3/2)x

Not quite

Given 6-(1/2)x=(3/5)+x = 6 - x/2 = 3/5 + x

Multiply through by 10 (2x5) yielding 60 - 5x = 6 + 10x or 15x = 54 or x = 54/15

Now try the other two you were given.

crappiefisher26

New member
See thats why i am gettin confused. The example doesnt show what you did. So im not sure if its right.

TchrWill

Full Member
1. (8/3)x-3=(2/3)x+15
2.(12/5)+7=31-(3/5)x

heres the example they give me. still cant figure it out though

Solve for x.

6-(1/2)x=(3/5)+x

it says ya need to isolate the variable x. We first add (1/2)x to both sides and subtract (3/5) from both sides

then they got 6-(3/5)=x+(1/2)x

(27/5)=(3/2)x

(2/3) times (27/5)=(2/3)times(3/2)x

Given 6-(1/2)x=(3/5)+x or 6 - x/2 = 3x/5 + x

Get rid of the fractions by multiplying through by any number that both 2 and 5 divide into evenly which is 10.

Collect like terms and solve for x.

Denis

Senior Member
Crappy, TchrWill was trying to show you an easier way!

crappiefisher26 said:
"6 - (1/2)x = (3/5) + x
it says ya need to isolate the variable x. We first add (1/2)x to both sides and subtract (3/5) from both sides"

OK, add (1/2)x to both sides: 6 = 3/5 + x + (1/2)x
NOW, subtract 3/5 from both sides: 6 - 3/5 = x + (1/2)x

So now we got what they got:
"then they got 6 - (3/5) = x + (1/2)x"

"So (27/5)=(3/2)x
(2/3) times (27/5)=(2/3)times(3/2)x"

What THEY did here was isolate the x by multiplying by 2/3: 3/2 * 2/3 = 1
So (2/3) * (27/5) = x
54/15 = x
18/5 = x

AND I think that THEY should be shot at sunrise for giving such complicated
steps in solving something simple :evil:
6 - (1/2)x = (3/5) + x
TchrWill told you to multiply each term by 10; that gets rid of fractions:
60 - 5x = 6 + 10x