Question

The reciprocal of 5 less than a number is 4 times the reciprocal of twice the number. find the number.

Answer 1

5 less than the number is x - 5
The reciprocal is 1/(x - 5)

This number is 1/(x - 5) = 4(1/(2x)) Cross multiply.
2x = 4*(x - 5) Remove the brackets.
2x = 4x - 20 Subtract 2x from both sides
0 = 4x - 2x - 20
0 = 2x - 20 Add 20 to both sides
20 = 2x Divide by 2
20/2 = x
10 = x