Let's go through each question and identify the correct answers:
1. **What property of inequality justifies the steps shown in the following solution process?**
- From: \(43d \geq -20\)
- To: \(34(43)d \geq -20(34)\)
- Result: \(d \geq -15\)
Here, since both sides are multiplied by a positive number (34), we should use the **Multiplication Property of Inequality**.
**Answer: Multiplication Property of Inequality**
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2. **What property of inequality can justify the math in Step 2?**
- Step 1: \(-6(3w - 7) > -66\)
- Simplified: \(-18w + 42 > -66\)
- Step 2: \(-18w + 42 - 42 > -66 - 42\)
- Result: \(-18w > -108\)
Here, in Step 2, we are subtracting 42 from both sides, which justifies using the **Subtraction Property of Inequality**.
**Answer: Subtraction Property of Inequality**
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3. **Based on their statements regarding the inequality \(56x \leq -10\), which combination of people is correct?**
- Juana says the inequality must be reversed because there is a negative sign.
- Anish believes the Multiplication or Division Property must be applied.
- Giselle says the inequality symbol must stay the same.
Since both Juana and Anish misinterpret the situation (the sign does not change simply due to being negative on one side), **Giselle** is actually the one who is correct—the direction of the inequality does not change. Thus, **only Giselle is correct**.
**Answer: Giselle**
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4. **What inequality does the number line graph?**
- A closed point at \(-7\) with an arrow extending left indicates values less than or equal to \(-7\).
**Answer: \(x \leq -7\)**
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5. **Graph \(x > 11\)**:
- An open point at 11 with an arrow extending indefinitely to the right indicates that \(x\) can take any value greater than 11.
**Answer: A number line ranges from 5 to 15 in increments of 1. An open point is plotted at 11. An arrow extends indefinitely right from the open point past 15 along the number line.**
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I hope this helps clarify the solutions! Let me know if you have any further questions.