Let's solve the inequality step-by-step:
Given:
[tex]\[
-0.4x - 10 > 14
\][/tex]
1. Add 10 to both sides:
[tex]\[
-0.4x - 10 + 10 > 14 + 10
\][/tex]
[tex]\[
-0.4x > 24
\][/tex]
2. Divide both sides by -0.4:
When dividing by a negative number, we must remember to reverse the inequality sign.
[tex]\[
x < \frac{24}{-0.4}
\][/tex]
Perform the division:
[tex]\[
x < -60
\][/tex]
So, the correct steps to solve the inequality [tex]$-0.4 x - 10 > 14$[/tex] result in [tex]$x < -60$[/tex].
Examining the provided solutions, we see that the correct work is in the second option:
[tex]\[
\begin{aligned}
-0.4 x-10 & >14 \\
-0.4 x & >24 \\
x & >-60 \\
\end{aligned}
\][/tex]
However, the final inequality should have been [tex]$x < -60$[/tex]. The intermediate steps shown are appropriate, except for the error in the direction of the inequality sign after division.
To conclude, the steps shown in the second option are closest to the correct procedure, but with a sign error in the final inequality. The correct final inequality should be [tex]$x < -60$[/tex].
