Write an equation and solve to find the numbers and show work.
9. Doubling the difference between a number and 4 is 6 more than the number.
Let's call the number we're trying to find "x".
The difference between "x" and 4 is "x - 4".
We're told to double that difference:
2(x-4)
And we're told that this equals 6 more than the original number "x":
2(x-4) = x + 6
Now we need to solve for "x".
First, distribute the 2 on the left side of the equation:
2x - 8 = x + 6
Then, subtract "x" from both sides of the equation:
x - 8 = 6
Add 8 to both sides:
x = 14
Therefore, the number we are looking for is 14.