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

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