SOLUTION: 2.Max was solving the equation below and isn’t sure if his answer is correct. Explain to Max how he can check his answer and then help him identify any errors he made. Provide the

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: 2.Max was solving the equation below and isn’t sure if his answer is correct. Explain to Max how he can check his answer and then help him identify any errors he made. Provide the       Log On


   

Question 943201: 2.Max was solving the equation below and isn’t sure if his answer is correct. Explain to Max how he can check his answer and then help him identify any errors he made. Provide the correct solution in your explanation.



3(3x+6) = 4(7x−1)
9x+18 = 28x−1
9x−9x+18 = 28x−9x−1
18 = 19x−1
18+1 = 19x−1+1
19 = 19x
1 = x

Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
He can check by substituting (1) for x.

3(3x+6) = 4(7x−1) 
3(3·1+6) = 4(7·1−1)
3(3+6) = 4(7-1)
3(9) = 4(6)
27 = 24

False so there is a mistake.


3(3x+6) = 4(7x−1) 
9x+18 = 28x−1        <--should be   9x+18 = 28x−4
9x−9x+18 = 28x−9x−1  <--should be   9x−9x+18 = 28x−9x−4
18 = 19x−1           <--should be   18 = 19x-4
18+1 = 19x−1+1       <--dhould be   18+4 = 19x-4+4 
19 = 19x             <--should be   22 = 19x 
1 = x                <--should be   22%2F19 = x

Common error in distributing: A(B + C), forgetting to 
multiply the A by the C.

Check the terribly ugly answer 22%2F19

3%283x%2B6%29%22%22=%22%224%287x-1%29

3%283%2822%2F19%29%5E%22%22%2B6%29%22%22=%22%224%287%2822%2F19%29%5E%22%22-1%29

3%28%2866%2F19%29%5E%22%22%2B6%29%22%22=%22%224%28%28154%2F19%29%5E%22%22-1%29

3%28%2866%2F19%29%5E%22%22%2B%286%2F1%29%29%22%22=%22%224%28%28154%2F19%29%5E%22%22-%281%2F1%29%29

3%28%2866%2F19%29%5E%22%22%2B%28%286%2A19%29%2F%281%2A19%29%29%29%22%22=%22%224%28%28154%2F19%29%5E%22%22-%28%281%2A19%29%2F%281%2A19%29%29%29

3%28%2866%2F19%29%5E%22%22%2B%28114%2F19%29%29%22%22=%22%224%28%28154%2F19%29%5E%22%22-%28%2819%29%2F%2819%29%29%29

3%28%2866%2B114%29%2F19%29%29%22%22=%22%224%28%28154-19%29%2F%2819%29%29%29

3%28%28180%29%2F19%29%29%22%22=%22%224%28%28135%29%2F%2819%29%29%29

540%2F19%22%22=%22%22540%2F19

Trouble is, when you get a terribly ugly solution such as 22%2F19,
to check the terribly ugly answer is much harder than solving
the equation.

Edwin