1. What property of inequality justifies the steps shown in the following solution process?

Question

43d≥−20

34(43)d≥−20(34)

d≥−15

(1 point)
Responses

Addition Property of Inequality
Addition Property of Inequality

Subtraction Property of Inequality
Subtraction Property of Inequality

Division Property of Inequality
Division Property of Inequality

Multiplication Property of Inequality
Multiplication Property of Inequality
Question 2
2. 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

Division Property of Inequality
Division Property of Inequality

Addition Property of Inequality
Addition Property of Inequality

Multiplication Property of Inequality
Multiplication Property of Inequality

Subtraction Property of Inequality
Subtraction Property of Inequality
Question 3
3. 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

Anish, Juana, and Giselle
Anish, Juana, and Giselle

Juana and Anish
Juana and Anish

Giselle and Juana
Giselle and Juana

Giselle and Anish
Giselle and Anish
Question 4
4. Use the image to answer the question.

What inequality does the number line graph?

(1 point)
Responses

x<−7
x<−7

x≤−7
x is less than or equal to negative 7

x≥−7
x is greater than or equal to negative 7

x>−7
x is greater than negative 7
Question 5
5. Graph x>11
(1 point)
Responses

Answer 1

Sure! Here are the responses to each question based on your provided information:

Question 1:

Property of Inequality: Multiplication Property of Inequality - It allows you to multiply both sides of an inequality by a positive number without changing the direction of the inequality.

Question 2:

Property of Inequality: Subtraction Property of Inequality - It allows you to subtract the same number from both sides of an inequality without changing the direction of the inequality.

Question 3:

Combination of People Correct: Anish, Juana, and Giselle - Anish's reasoning is correct because the Multiplication or Division Property of Inequality applies when dealing with negative numbers. Juana's statement that it must be reversed is incorrect, and Giselle is also incorrect in her statement that the inequality stays the same because we need to apply the multiplication/division property when dividing by a negative.

Question 4:

Inequality represented by the number line: x<−7 - The number line shows all values less than -7 (unless there is a closed circle at -7, then it would be x ≤ -7).

Question 5:

Graph x>11: You would draw a number line and shade to the right of 11, with an open circle at 11 (indicating that 11 is not included).

If you want further clarification or additional questions, feel free to ask!