How can we solve the equation 7/8 – 1/x = 3/4 for x?

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Solving the Equation: 7/8 – 1/x = 3/4

To solve the equation 7/8 – 1/x = 3/4, let’s break it down step by step.

Step 1: Isolate the Fraction

First, we want to isolate the fraction involving x. To do this, we can subtract 3/4 from both sides of the equation:

7/8 - 1/x - 3/4 = 0

Next, we need a common denominator to combine 7/8 and -3/4. The common denominator here is 8, so we rewrite 3/4:

3/4 = 6/8

Now, substitute this back into our equation:

7/8 - 6/8 - 1/x = 0

Which simplifies to:

1/8 - 1/x = 0

Step 2: Rearrange the Equation

Now we rearrange the equation to isolate 1/x: 1/x = 1/8.

Step 3: Solve for x

To find x, we can take the reciprocal of both sides:

x = 8

Final Answer

The solution to the equation 7/8 – 1/x = 3/4 is x = 8.

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