How do you solve for x in the equation 3/4 * x = 5/8 + 4x?

Solving for x in the equation 3/4 * x = 5/8 + 4x

To solve the equation 3/4 * x = 5/8 + 4x, we’ll go through the steps carefully:

1. Isolate the variable x:

   First, we want to get all terms involving x on one side of the equation. To do this, we can subtract 4x from both sides:

   3/4 * x - 4x = 5/8

2. Combine like terms:

   The left side has 3/4 * x and -4x. We can express -4x as -16/4x to have a common denominator:

   3/4 * x - 16/4 * x = 5/8

   (3/4 - 16/4) * x = 5/8

   -13/4 * x = 5/8

3. Multiply by the reciprocal:

   Now, to solve for x, we need to multiply both sides by the reciprocal of -13/4, which is -4/13:

   x = (5/8) * (-4/13)

4. Simplify the equation:

   Now we’ll multiply the fractions:

   x = -20/104

   Next, simplify the fraction:

   -20/104 = -5/26

Final Result:

The solution for x is:
x = -5/26