Question

State the inverse operation. Multiply by \(-2\)

Short answer

The inverse operation is 'divide by -2'.

Step-by-step solution

Identify the effect of the original operation

The given operation is 'multiply by -2'. When a number is multiplied by -2, two things happen: first, the number doubles, and then its sign changes. For example, if we take a number 3, when it is multiplied by -2 we get -6; the number 3 has not only doubled to 6, but its sign has also changed from positive to negative.

Find the inverse operation

The inverse operation should undo the changes caused by the original operation. So the inverse of 'multiply by -2' should divide the result by 2 and then change its sign; this operation is defined as 'divide by -2'. For instance, if we apply the operation 'divide by -2' to -6, it undoes the changes caused by 'multiply by -2', returning us to the original number 3.