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
Subtraction Property of Inequality
Subtraction Property of Inequality
Division Property of Inequality
Division Property of Inequality
Addition Property of Inequality
Addition Property of Inequality
Multiplication Property of Inequality
Multiplication Property of 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
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
Addition Property of Inequality
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Subtraction Property of Inequality
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
Giselle and Anish
Giselle and Anish
Giselle and Juana
Giselle and Juana
Anish, Juana, and Giselle
Anish, Juana, and Giselle
Juana and Anish
The correct combination of people is Giselle and Anish.
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 less-than-or-equal-to negative 7
x<−7
x less than negative 7
x≥−7
The inequality represented by the number line graph is x < -7.
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 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.
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 right from the closed 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 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 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.