Chapter 1.3, Problem 54PPSE

Solution

To state: The correct answer if you have mistakenly subtracted $b\text{from}a$ instead of subtracting $a\text{from}b$ .

The resultant answer after subtracting $b\text{from}a$ is negative inverse of the correct answer $a-b$ .

Given information:

The given statement says to subtract $a\text{from}b$ .

Explanation:

Consider the definition of algebraic expression:

The given statement says to subtract $b\text{from}a$ which means $b-a$ .

But mistakenly $a\text{from}b$ was subtracted which means $a-b$ .

The wrong answer is negative (additive inverse) of the correct answer.

It can be shown as:

  $a-b$

Take minus common and use Distributive property,

  $-\left(a+b\right)$

Use Commutative property,

  $-\left(b-a\right)$

Therefore, it is proved that the result got mistakenly is negative inverse of the correct answer.