Find the first wrong line
A solution has four lines. The last answer does not fit the first line. One line went wrong. Which one?
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- Four lines of a worked solution.
- Line 1 to line 2: left side
+ 4, right side− 4. - The sides were treated differently. Line 2 is the slip.
- Mend it: add 4 to both sides,
6c = 2c + 16.
Read down the lines
Line 2 is the first wrong line. It is the slip, a small mistake.
Line 1 is 6c − 4 = 2c + 12. Line 2 is 6c = 2c + 8. Lines 3 and 4 are 4c = 8 and c = 2.
Ask of each line: what happened to the left? What happened to the right?
From line 1 to line 2, the left side lost its − 4. That is adding 4. The right side went from 12 to 8. That is taking 4 off. The two sides were not treated alike.
Test it. The last answer is 2. It does not fit line 1: left 8, right 16. The first line is true at c = 4. Put 4 into line 2: left 24, right 16. It does not fit.
Mend line 2: add 4 to both sides of line 1. You get 6c = 2c + 16. Take 2c off both sides: 4c = 16. Share by 4: c = 4.
Rule: A line whose answer differs from the line before is wrong. The first such line is the slip.