Find the missing number so that the equation has no solutions.–5x–7=x+1

Sure, let's solve this step by step:

1. First, we need to get all the x terms on one side of the equation and the constants on the other side. So, let's add 5x to both sides of the equation to get rid of -5x on the left side:

   -5x + 5x - 7 = x + 5x + 1 This simplifies to: -7 = 6x + 1

2. Next, let's subtract 1 from both sides to isolate the x term:

   -7 - 1 = 6x + 1 - 1 This simplifies to: -8 = 6x

3. Finally, let's divide both sides by 6 to solve for x:

   -8/6 = x Simplifying the fraction gives us: x = -4/3

So, the missing number that makes the equation have no solutions is not a single number. The equation as given has a solution of x = -4/3. If you want the equation to have no solutions, you would need to change the equation so that the x terms cancel out and the constants do not, such as -5x - 7 = -5x + 1.