Chapter 4.5, Problem 46HP

To determine

To find: whether T or E is right.

Answer to Problem 46HP

Both of them are wrong.

Explanation of Solution

Given:

T   $\begin{array}{c}7-2x=-51\\ 7+7-2x=-51+7\\ 2x=-44\\ \frac{2x}{2}=\frac{-44}{2}\\ x=-22\end{array}$

E   $\begin{array}{c}7-2x=-51\\ -7+7-2x=-51+\left(-7\right)\\ -2x=-58\\ \frac{-2x}{-2}=\frac{-58}{-2}\\ x=-29\end{array}$

Calculation:

E solves wrongly $x=-29$ (This is wrong because $-58$ divided by $-2$ is 29)

T is wrong because she adds 7 in $2^{nd}$ step in place of subtracting

  $7+7-2x=-51+7$ which is wrong.

The correct way is

  $\begin{array}{c}7-2x=-51\\ -7+7-2x=-51+\left(-7\right)\\ -2x=-58\\ \frac{-2x}{-2}=\frac{-58}{-2}\\ x=29\end{array}$

Conclusion:

Therefore, neither of them is correct.