Meaning Preservation Math Example 1

Solution

1. 1
   Start: $x+5=12$. Solution set: $\{7\}$ (to be found).
2. 2
   Step 1: subtract 5 from both sides: $x+5-5 = 12-5$. This is valid because subtracting the same value from both sides of an equation preserves equality.
3. 3
   Step 2: simplify: $x = 7$. The solution set is $\{7\}$.
4. 4
   Every step was an equivalence-preserving operation — the solution set $\{7\}$ was preserved throughout.