The problem is asking to set up an inequality to determine how many hours Juanita must work to afford new shoes, given:

• She has $25.
• She earns $11 per hour.
• She needs at least $58 to buy new shoes.

Let $h$ represent the number of hours Juanita needs to work. Juanita’s total earnings would be her hourly wage, $11, multiplied by the number of hours she works, $h$, plus the $25 she already has. This total needs to be greater than or equal to $58 (since she needs at least $58).

The inequality can be set up as:

$11h + 25 \geq 58$

Now, we can solve this inequality to find $h$.

1. Subtract 25 from both sides: $11h \geq 58 - 25$ $11h \geq 33$

2. Divide both sides by 11: $h \geq \frac{33}{11}$ $h \geq 3$

Therefore, Juanita must work at least 3 hours to have enough money to buy the shoes.

Would you like further explanation or have any questions? Here are some related questions to explore further:

1. How can we solve inequalities with variables on both sides?
2. What happens if Juanita needs exactly $58 instead of at least $58?
3. How do you interpret the meaning of an inequality in a real-life scenario?
4. What is the difference between an equation and an inequality in this case?
5. How can we apply this method to other real-life budgeting situations?

Tip: When solving inequalities, always be mindful of whether you need to reverse the inequality symbol when multiplying or dividing by negative numbers.