What property of inequality justifies the steps shown in the following solution process? 43d≥−20 34(43)d≥−20(34) d≥−15 (1 point) Responses Division Property of Inequality Division Property of Inequality Multiplication Property of Inequality Multiplication Property of Inequality Addition Property of Inequality Addition Property of Inequality Subtraction Property of Inequality

The property of inequality that justifies the steps shown in the solution process is the **Multiplication Property of Inequality**.

In the solution, multiplying both sides of the inequality \( 43d \geq -20 \) by \( 34 \) is valid as long as \( 34 \) is positive, which it is. Thus, the multiplication maintains the direction of the inequality.

What property of inequality can justify the math in Step 2? Step 1: −6(3w−7)>−66 −18w+42>−66 Step 2: −18w+42−42>−66−42 −18w>−108 Step 3: −18w−18>−108−18 w<6 (1 point) Responses Addition Property of Inequality Addition Property of Inequality Division Property of Inequality Division Property of Inequality Subtraction Property of Inequality Subtraction Property of Inequality Multiplication Property of Inequality

The property of inequality that justifies the math in Step 2 is the **Subtraction Property of Inequality**.

In Step 2, you subtract 42 from both sides of the inequality, which is allowed according to the Subtraction Property of Inequality, as it states that if you subtract the same number from both sides of an inequality, the direction of the inequality remains the same.

Juana, Anish, and Giselle are comparing their solutions to the inequality 56x≤−10 . Juana says that the inequality symbol must be reversed because there is a negative sign in the inequality. Anish says the Multiplication Property of Inequality or Division Property of Inequality must be applied. Giselle says the inequality symbol must stay the same. Based on these answers, which combination of people is correct? (1 point) Responses Juana and Anish Juana and Anish Giselle and Anish Giselle and Anish Anish, Juana, and Giselle Anish, Juana, and Giselle Giselle and Juana

To solve the inequality \( 56x \leq -10 \), we need to divide both sides by 56. Here’s the breakdown:

1. **Giselle** is correct in saying that the inequality symbol must stay the same when you divide by a positive number (56 is positive), so the inequality remains \( x \leq -\frac{10}{56} \) or simplified, \( x \leq -\frac{5}{28} \).

2. **Anish** is also correct in stating that the Multiplication Property of Inequality or Division Property of Inequality must be applied, as dividing both sides of the inequality by a positive number does not reverse the inequality.

3. **Juana** is incorrect because the inequality symbol does not need to be reversed; only when dividing (or multiplying) by a negative number does the inequality symbol need to be reversed.

Based on this interpretation, the correct combination of people is **Giselle and Anish**.

Use the image to answer the question. What inequality does the number line graph? (1 point) Responses x≤−7 x less-than-or-equal-to negative 7 x≥−7 x greater-than-or-equal-to negative 7 x<−7 x less than negative 7 x>−7

To determine the inequality represented by a number line graph, we need to look for the following key features:

1. **Filled Circle vs. Open Circle**:
- **Filled (or closed) circle** at a point indicates that the number is included in the solution ( ≤ or ≥).
- **Open circle** at a point indicates that the number is not included in the solution ( < or >).

2. **Direction of Arrow or Line**:
- If the line or arrow points to the left, the inequality is less than (< or ≤).
- If the line or arrow points to the right, the inequality is greater than (> or ≥).

Without the actual image, I cannot directly assess the number line. However, based on common conventions:

- If the number line has a filled circle at -7 and extends to the left, the inequality would be \( x \leq -7 \).
- If it has an open circle at -7 and extends left, the inequality would be \( x < -7 \).
- If there is a filled circle at -7 and the line extends to the right, the inequality would be \( x \geq -7 \).
- If there is an open circle at -7 and the line extends right, the inequality would be \( x > -7 \).

If you can provide details about whether the circle is open or closed and the direction of the line, I can help you more accurately determine the inequality!

it is a -7 going past -12

Based on your description, it seems we have:

- A point at \(-7\),
- That point is likely in a **closed circle** (otherwise you wouldn't mention it being "at" -7), indicating that -7 is included in the solution set,
- The line extends in the **left direction** (past -12), indicating all values less than -7 are included.

Given this information, the appropriate inequality representing the number line graph would be:

**\( x \leq -7 \)**

So, the answer is: **x ≤ −7**.

Graph x>11 .

To graph the inequality \( x > 11 \), follow these steps:

1. **Draw a number line**:
- Create a horizontal line with evenly spaced tick marks. Label at least the point \( 11 \).

2. **Plot the point at \( 11 \)**:
- Since the inequality is \( x > 11\), place an **open circle** at \( 11 \). The open circle signifies that \( 11\) is not included in the solution set.

3. **Shade the area to the right of \( 11 \)**:
- Draw an arrow or shade the number line to the right of \( 11\) to indicate that all numbers greater than \( 11 \) are part of the solution.

This visually represents the inequality \( x > 11 \).

If you were to visualize it:
- The open circle at \( 11 \) and the shading extending to the right indicates that all numbers greater than \( 11 \) satisfy the inequality.