Chapter 8.7, Problem 30PPS

To determine

Sandrea and Fernando are solving $4a-5b=7$ for b. Either of them correct.

Explanation of Solution

Given information:

  $4a-5b=7$

  $\begin{array}{l}\text{Sandrea}\\ 4a-5b=7\\ -5b=7-4a\\ \frac{-5b}{-5}=\frac{7-4a}{-5}\\ b=\frac{7-4a}{-5}\end{array}$  $\begin{array}{l}\text{Fernando}\\ 4a-5b=7\\ 5b=7-4a\\ \frac{5b}{5}=\frac{7-4a}{5}\\ b=\frac{7-4a}{5}\end{array}$

Calculation:

Comparing their solutions line by line. In the first line both Sandrea and Fernando have the problem written, in the second line there is a difference in their solution. Sandrea has $-5a=7-4a$ while Fernando has $5a=7-4a$ .The given equation is $4a-5b=7$ there is - 5b, and that Fernando has made a mistake.

Following the rest of their solutions, there is no further mistakes are made, however the one error that Fernando made in the second line given him the wrong solution.

Sandrea is correct because every steps are correctly performed. Fernando omitted the negative sign from - 5b .