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

Subtraction Property of Inequality
Subtraction Property of Inequality

Addition Property of Inequality
Addition Property of Inequality

Division Property of Inequality
Division Property of Inequality

Multiplication Property of Inequality

Answer 1

The solution process involves multiplying both sides of the inequality \( 43d \geq -20 \) by 34. The property that justifies this step is:

Multiplication Property of Inequality.

This property states that if you multiply both sides of an inequality by a positive number, the inequality remains valid. Since 34 is a positive number, this step is justified by the Multiplication Property of Inequality.

Answer 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

Subtraction Property of Inequality
Subtraction Property of Inequality

Multiplication Property of Inequality
Multiplication Property of Inequality

Addition Property of Inequality

Answer 3

The justification for the math in Step 2, where you subtract 42 from both sides of the inequality \( -18w + 42 > -66 \), is:

Subtraction Property of Inequality.

This property states that you can subtract the same number from both sides of an inequality without changing the direction of the inequality. In this case, subtracting 42 from both sides is justified by the Subtraction Property of Inequality.

Answer 4

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

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

Giselle and Juana
Giselle and Juana

Giselle and Anish

Answer 5

To solve the inequality \( 56x \leq -10 \), we can divide both sides by 56. Since 56 is a positive number, the inequality symbol will not change.

• Juana's claim that the inequality symbol must be reversed because there is a negative sign in the inequality is incorrect. The presence of a negative number on the right side does not dictate a reversal of the symbol in this case until we perform a division by a negative number, which is not the case here.

• Anish's claim that either the Multiplication Property of Inequality or the Division Property of Inequality must be applied is correct. We would indeed use the Division Property of Inequality to simplify the equation.

• Giselle's claim that the inequality symbol must stay the same is correct because we are dividing by a positive number (56), therefore the direction of the inequality does not change.

Based on this analysis, the correct combination is:

Giselle and Anish.

Answer 6

Use the image to answer the question.

A number line ranges from negative 12 to 0 in increments of 1. A closed point is plotted at negative 7. An arrow extends indefinitely left from the closed point past negative 12 along the number line.

What inequality does the number line graph?

(1 point)
Responses

x>−7
x greater than negative 7

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

x<−7
x less than negative 7

x≤−7

Answer 7

The number line you described has a closed point at \(-7\) and an arrow extending indefinitely to the left. This means that the values of \(x\) are less than or equal to \(-7\), since \(x\) can be equal to \(-7\) (due to the closed point) and it can also be any number less than \(-7\) (indicated by the arrow extending to the left).

Thus, the correct inequality represented by the number line graph is:

\(x \leq -7\) (x less than or equal to negative 7).

Answer 8

Graph x>11.(1 point)
Responses

A number line ranges from 5 to 15 in increments of 1. An open point is plotted at 11. An arrow extends indefinitely left from the open point past 5 along the number line.
Image with alt text: A number line ranges from 5 to 15 in increments of 1. An open point is plotted at 11. An arrow extends indefinitely left from the open point past 5 along the number line.

A number line ranges from 5 to 15 in increments of 1. A closed point is plotted at 11. An arrow extends indefinitely left from the closed point past 5 along the number line.
Image with alt text: A number line ranges from 5 to 15 in increments of 1. A closed point is plotted at 11. An arrow extends indefinitely left from the closed point past 5 along the number line.

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.
Image with alt text: 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.

A number line ranges from 5 to 15 in increments of 1. A closed point is plotted at 11. An arrow extends indefinitely right from the closed point past 15 along the number line.

Answer 9

To graph the inequality \( x > 11 \):

• You would place an open point at \( 11 \) to indicate that \( 11 \) itself is not included in the solution (because it is a "greater than" inequality).
• The arrow should extend indefinitely to the right from the point at \( 11 \) to indicate that all values greater than \( 11 \) are part of the solution.

Based on this description, the correct graph representation is:

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.

This corresponds to the third option you've provided.