-2(x+7)-5x = -6x-x -2x-14-5x = -7x <-- we distributed to remove (); combined like terms -7x-14 = -7x +14 +14 <-- we added 14 to both sides ---------------- -7x = -7x+14 7x 7x <-- we added 7x to both sides ---------------- 0 = 14 Since 0 does not equal to 14 there are no solutions. Rule: When all the letters cancel out and there is only a number left on both sides: 1. If the numbers on the two sides are EQUAL, there are INFINITELY MANY solutions. The equation is said to be an IDENTITY. 2. If the numbers on the two sides are BOT equal, there are NO solutions. The equation is said to be a CONTRADICTION. Your equation was a CONTRADICTION. Edwin