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
To check substitute 1 for x in the
original equation:
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
So it's incorrect. So we look for the error:
3(3x+6) = 4(7x-1)
9x+18 = 28x-1 <-- There it is! That -1 should be a -4
9x-9x+18 = 28x-9x-1
18 = 19x-1
18+1 = 19x-1+1
19 = 19x
1 = x
So the error was in the first step. When distributing on the
right to remove the parentheses, he multiplied 4 by the 7x but
he forgot to multiply 4 by the -1, and just left it -1. It
should have been -4.
Correction:
3(3x+6) = 4(7x-1)
9x+18 = 28x-4 <-- Got it right this time!
9x-9x+18 = 28x-9x-4
18 = 19x-4
18+4 = 19x-4+4
22 = 19x
22 = 19x
= x <--- what a god-awful answer!!
Checking:
The god-awful answer is correct. But it was
murder to check it! J
Edwin