Part A:
Since Juanita had at first $25
Since she earns $11 per hour
Then her total earning in x hours is
![11x+25](https://img.qammunity.org/2023/formulas/mathematics/high-school/kdmvlh9nc164t224gewqjmb3v4ma3eq3i8.png)
Since she needs at least $58 to buy new shoes
At least means greater than or equal, then the inequality should be
![11x+25\ge58](https://img.qammunity.org/2023/formulas/mathematics/high-school/e5wzor1tcj5qnssm3ted6cvzjwmt5o84sz.png)
Part B:
Let us solve it by subtracting 25 from each side
![\begin{gathered} 11x+25-25\ge58-25 \\ 11x\ge33 \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/high-school/ng38hurwgmmlle4bvisont9pq7hzjac8y5.png)
Divide each side by 11
![\begin{gathered} (11x)/(11)\ge(33)/(11) \\ x\ge3 \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/high-school/3b17fao23zd7d2gulxupbnl6eo5ur0fvbx.png)
Then the answer is the 3rd choice