Question

Janet solved the following inequality incorrectly, but she cannot figure out where she went wrong. Find Janet's mistake and write a note to her to help her solve the inequality correctly . Janet's Solution and Work: x/5 + 4 > - 3x/5 > 1x < 5

Answer 1

Janet add 4 to both sides

Janet swapped the sign

The note for Janet:

Janet, when we need to isolate the x-term we need to cancel out the non-x-terms, that's why we subtract 4 from both sides since 4 -4 = 0

1) Consider that the steps to solve for x this inequality is:

$\begin{gathered} \frac{x}{5}+4>-3 \\ \frac{x}{5}+4-4>-3-4 \\ \frac{x}{5}>-7\text{ }\times5 \\ x>-35 \end{gathered}$

2) Note that Janet when she was isolating the x term committed a mistake shed didn't add -4 to both sides. She added 4 to both sides and swapped the sign from greater than to lesser than.

3) Hence, the answer is:

Janet add 4 to both sides

Janet swapped the sign

The note for Janet:

Janet, when we need to isolate the x-term we need to cancel out the non-x-terms, that's why we subtract 4 from both sides since 4 -4 = 0