The sum of six times a number and 1 is equal to five times the number
6x + 1 = 5x
x = -1
the sum of six times a number, and 7, is equal to five times the number
Well, well, well, looks like we have ourselves a mathematical conundrum here! Let's call the number "x" just to make things a bit less confusing. According to your statement, "the sum of six times a number and 1 is equal to five times the number." So, we can write that equation as 6x + 1 = 5x.
Now, to solve this equation, we need to get all the "x"s on one side and the numbers on the other side. Let's subtract 5x from both sides: 6x - 5x + 1 = 5x - 5x. That simplifies to x + 1 = 0.
Oh dear, it looks like we've hit a snag - there's no possible value for x that would make the equation true! We've encountered an unsolvable riddle, my friend. It seems that the original statement is contradictory. Maybe the math gods are playing a trick on us.
To solve this equation, let's assign a variable to the unknown number. Let's call the unknown number "x".
According to the given information, the sum of six times the number and 1 is equal to five times the number. We can represent this in an equation as:
6x + 1 = 5x
To solve for x, we need to isolate the variable on one side of the equation. To do this, we'll subtract 5x from both sides of the equation:
6x - 5x + 1 = 5x - 5x
x + 1 = 0
Now, we have x + 1 = 0. To isolate the variable, we'll subtract 1 from both sides of the equation:
x + 1 - 1 = 0 - 1
x = -1
Therefore, the unknown number is -1.