Linear equation w/ several occurences of the variable

crappiefisher26

New member
Joined
Jul 23, 2006
Messages
49
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

answer is (18/5)x
 

TchrWill

Full Member
Joined
Jul 7, 2005
Messages
856
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

answer is (18/5)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
Joined
Jul 23, 2006
Messages
49
See thats why i am gettin confused. The example doesnt show what you did. So im not sure if its right.
 

TchrWill

Full Member
Joined
Jul 7, 2005
Messages
856
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

answer is (18/5)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
Joined
Feb 17, 2004
Messages
1,641
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

"answer is (18/5)x" : should be "answer is 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
Add 5x to both sides:
60 = 6 + 15x
subtract 6 from both sides:
54 = 15x
54/15 = x
18/5 = x

Now can you see how much easier that is :?: :?:
 
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