An integer decreases by 6 to become twice the integer minus 10. Find the integer.

Step-by-step solution

1. Step 1: Let the integer be $x$.
2. Step 2: Decrease by 6 gives $x-6$.
3. Step 3: Set this equal to twice the integer minus 10: $x-6=2x-10$.
4. Step 4: Move $x$ to one side: $x-6-2x=-10$.
5. Step 5: Simplify left side: $-x-6=-10$.
6. Step 6: Add $x$ to both sides: $-6=x-10$.
7. Step 7: Add 10 to both sides: $x=4$.
8. Step 8: Conclude the integer is 4.

Concept tested: Solving integer equations

Published 10 October 2026 · How this solution was prepared and checked