Question

Solve for x: 7 over 8 minus 1 over x equals 3 over 4

x = 1

x = 2

x = 4

x = 8

Answer 1

(7/8) - (1/x) = (3/4)

first set the equation equal to zero by subtracting 3/4 from both sides

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

next find the least common denominator (LCD), in this case, the LCD is 8x

multiply each individual term by the LCD (8x)

(7/8)*8x = 7x, the 8 is on both the top and the bottom, so it cancels out, the x is multiplied by the 7 because they are both on top

(1/x)*8x = 8, the x is on both the top and the bottom, so it cancels out, the 8 is multiplied by the 1 because they are both on top

(3/4)*8x = 6x, 8 divided by four equals two, because the greater number is on the top, the quotient is on the top, the x does not cancel out, so it is multiplied by the 2 to get 2x, which is then multiplied by the 3 to get 6x. You could also look at it like (3/4)*(8x/1), which equals 24x/4, or, again, 6x.

Now you have:
7x-8-6x = 0

combine like terms (the 7x and -6x) to get:

x-8 = 0

add eight to both sides

x = 8