To determine how many hours Genevieve needs to work, we can set up an inequality based on the information given.
- Genevieve currently has $56.
- She earns $12 per hour.
- She wants to have at least $200.
Let's denote the number of hours she needs to work as \( x \).
The total amount of money Genevieve will have after working \( x \) hours can be expressed as:
\[ \text{Total Money} = 56 + 12x \]
She wants this total to be at least $200:
\[ 56 + 12x \geq 200 \]
Now, we'll solve for \( x \):
- Subtract 56 from both sides:
\[ 12x \geq 200 - 56 \] \[ 12x \geq 144 \]
- Divide both sides by 12:
\[ x \geq \frac{144}{12} \] \[ x \geq 12 \]
Thus, the inequality that represents the number of hours Genevieve needs to work is:
\[ x \geq 12 \]
Your options seem incorrect since "x ≥ 12" isn't listed. However, if you're looking for a different interpretation or need clarification, please let me know!