Let's check the steps for Madlynn and Emilie separately to determine if they are correct.

Checking Madlynn's Work

Madlynn's Work	Steps	Is this Step Correct?
$\frac{4 x + 5}{- 2} - 1 > - 3$
$\frac{4 x + 5}{- 2} < - 2$	Add $1$ to both sides.	No

Madlynn's first step was to add $1$ to both sides of the inequality, and she did this correctly. However, she reversed the inequality, which is not correct when the same number is added to both sides.

Checking Emilie's Work

Emilie's Work	Steps	Is this Step Correct?
$\frac{4 x + 5}{- 2} - 1 > - 3$
$\frac{4 x + 5}{- 2} > - 2$	Add $1$ to both sides.	Yes
$4 x + 5 > 4$	Multiply both sides by $- 2 .$	No

Emilie's first step was correct, and for second step she multiplied both sides of the inequality by $- 2,$ which she did this correctly. However, she did not reverse the inequality, which she should have because she multiplied by a negative number

Conclusion

This means neither of them is correct. Both of them used the correct steps, but both made a mistake in identifying the correct direction of the inequality in one of the steps. Let's see the correct calculation.

\frac{4 x + 5}{- 2} - 1 > - 3

AddIneq

$LHS + 1 > RHS + 1$

\frac{4 x + 5}{- 2} > - 2

MultNegIneq

Multiply by $- 2$ and flip inequality sign

4 x + 5 < 4

SubIneq

$LHS - 5 < RHS - 5$

4 x < - 1

DivIneq

$LHS / 4 < RHS / 4$

x < - \frac{1}{4}

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