when 2 is subtracted from four times a certain number and then divided by 7, the result is the same as when 1 added to the number.What is the number
(4x-2)/7 = x+1
To solve this problem, we need to translate the given information into an equation.
Let's assume the certain number is represented by "x."
The first part of the problem states, "when 2 is subtracted from four times a certain number." This can be written as 4x - 2.
The second part says, "and then divided by 7." So, we divide the previous expression by 7, resulting in (4x - 2)/7.
The third part states, "the result is the same as when 1 added to the number." So, we add 1 to the certain number itself, which gives us x + 1.
Now, we have the equation (4x - 2)/7 = x + 1.
To solve for x, let's eliminate the fraction by multiplying both sides of the equation by 7:
7 * (4x - 2)/7 = 7 * (x + 1).
This simplifies to 4x - 2 = 7x + 7.
Next, let's isolate the variables on one side of the equation. Subtract 4x from both sides:
4x - 4x - 2 = 7x - 4x + 7.
Simplifying further, we have -2 = 3x + 7.
To solve for x, subtract 7 from both sides:
-2 - 7 = 3x + 7 - 7.
-9 = 3x.
Finally, divide both sides of the equation by 3:
-9/3 = 3x/3.
-3 = x.
Therefore, the certain number is -3.