To solve the equation 7/8 – 1/x = 3/4, we need to isolate x. Start by getting rid of the fractions.
First, let’s rewrite the equation for clarity:
7/8 – 1/x = 3/4
Next, we can eliminate the fractions by finding a common denominator. The common denominator of 8 and 4 is 8. To make things easier, let’s multiply through the entire equation by 8x (the product of the denominators):
8x(7/8) – 8x(1/x) = 8x(3/4)
This simplifies to:
7x – 8 = 6x
Now, we want to isolate x. Start by moving 6x to the left side of the equation:
7x – 6x – 8 = 0
This simplifies to:
x – 8 = 0
Finally, add 8 to both sides:
x = 8
So, the solution is x = 8. To check, substitute x back into the original equation:
7/8 – 1/8 = 3/4
This gives us:
6/8 = 3/4
Which simplifies to 3/4 = 3/4, confirming our solution. Thus, the value of x is indeed 8.