Talk:Solutions To Mathematics Textbooks/Basic Mathematics/Chapter 1

Chapter 1, Section 2, exercise 15 doesn't offer the correct solution.

{\displaystyle 2-x=5\,}{\displaystyle 2-x=5\,} {\displaystyle -x=3\,}{\displaystyle -x=3\,}

{\displaystyle x=-3\,}{\displaystyle x=-3\,}		multiply both sides by -1.

You can't multiply both sides by -1, because the section is talking about RULES FOR ADDITION.

Multiplication wasn't introduced yet in the book, neither it's properties, in this case called N7 [ (-1)a = a ]

The correct solution in this case is to use the introduced N3 and N2 rules.

From the point above:

-x = 3

-x+x = 3+x by N3, which let's you add the same term on both sides.

0 = 3+x by N2 which cancels opposite terms [ -x+x = 0 ]

Then, you need to use N3 again to have -3 on both sides and cancel 3-3 on the other side using N2.

0 = 3+x

-3 = 3-3+x

-3 = 0+x

-3 = x or x = -3

You can't use a tool that's not offered to solve a problem. You have to work with what's offered, that's the whole point of learning deduction and proofs.