It's important to know that reciprocals are the multiplicative inverse of a numbers, for example, the reciprocal of 7 is 1/7.
As you can observe, using reciprocals would help to solve equations when we have to get rid off a factor. For example, if we have the equations 4x = 8, we would use the reciprocal of 4 to isolate the variable x: (4x)/4 = 8/4 then x = 2.
Therefore, reciprocals are used to move factors across the equation to isolate the variable.