This amounts to working a problem backward: Start with the answer that you want to end up with: x = 24 Then multiply both sides by some arbitrary number, say -2 -2x = -48 Now add an arbitrary multiple of x, say 7x, to both sides: -2x + 7x = -48 + 7x Combine the terms on the left: 5x = -48 + 7x That one will do, but if you like you can add an arbitrary number to both sides, say 17 5x + 17 = -48 + 7x + 17 Combine -48 and 17 on the right side: 5x + 17 = -31 + 7x That one has the solution x = 24. You can make as many equations that have the solution x = 24 as you like, choosing different arbitrary numbers from the ones I chose. Edwin