Question
Solve the inequality Rx>10, where R is a number greater than 0.
x blank blank over R
x blank blank over R
Answers
Answer
Solve the inequality Ay+3<12, where A is a number greater than 0
y blank blank over A
y blank blank over A
Answer
Jorelle is planning a 5-day vacation. The trip will cost him $1,300.00 for airfare, food, and itineraries. He plans to stay in a hotel room for $80.00 per night. He only has $950.00 in savings, but he earns $25.00 per hour from his online tutoring services. Create a linear inequality in one variable that would best translate the problem. Determine the minimum number of hours Jorelle must tutor so he can have enough money for the trip.
Responses
950+25x≥1,700; at least 30 hours
950 plus 25 x greater-than-or-equal-to 1,700 ; at least 30 hours
950+25x≥1,300; at least 14 hours
950 plus 25 x greater-than-or-equal-to 1,300 ; at least 14 hours
950+25x≤1,700; at most 30 hours
950 plus 25 x less-than-or-equal-to 1,700 ; at most 30 hours
950+25x≤1,300; at most 14 hours
Responses
950+25x≥1,700; at least 30 hours
950 plus 25 x greater-than-or-equal-to 1,700 ; at least 30 hours
950+25x≥1,300; at least 14 hours
950 plus 25 x greater-than-or-equal-to 1,300 ; at least 14 hours
950+25x≤1,700; at most 30 hours
950 plus 25 x less-than-or-equal-to 1,700 ; at most 30 hours
950+25x≤1,300; at most 14 hours
Answer
Mary Ann solves the inequality −3x≥12. Justify the steps Mary Ann takes to find the solution set.(1 point)
Responses
Mary Ann adds −3 to both sides of the inequality and changes the inequality symbol to ≤ to get x≤9.
Mary Ann adds negative 3 to both sides of the inequality and changes the inequality symbol to less-than-or-equal-to to get x less-than-or-equal-to 9 .
Mary Ann divides both sides of the inequality by −3 to get x≥−4.
Mary Ann divides both sides of the inequality by negative 3 to get x greater-than-or-equal-to negative 4 .
Mary Ann adds −3 to both sides of the inequality to get x≥9.
Mary Ann adds negative 3 to both sides of the inequality to get x greater-than-or-equal-to 9 .
Mary Ann divides both sides of the inequality by −3 and changes the inequality symbol to ≤ to get x≤−4.
Responses
Mary Ann adds −3 to both sides of the inequality and changes the inequality symbol to ≤ to get x≤9.
Mary Ann adds negative 3 to both sides of the inequality and changes the inequality symbol to less-than-or-equal-to to get x less-than-or-equal-to 9 .
Mary Ann divides both sides of the inequality by −3 to get x≥−4.
Mary Ann divides both sides of the inequality by negative 3 to get x greater-than-or-equal-to negative 4 .
Mary Ann adds −3 to both sides of the inequality to get x≥9.
Mary Ann adds negative 3 to both sides of the inequality to get x greater-than-or-equal-to 9 .
Mary Ann divides both sides of the inequality by −3 and changes the inequality symbol to ≤ to get x≤−4.
Answer
Which of the following shows how to solve the linear inequality with a letter coefficient Hy<7, where H is a number greater than 0?
Responses
y<7H
y less than 7 upper H
y<7H
y less than Start Fraction 7 over upper H End Fraction
Hy<7
upper H y less than 7
y<7
Responses
y<7H
y less than 7 upper H
y<7H
y less than Start Fraction 7 over upper H End Fraction
Hy<7
upper H y less than 7
y<7
Answer
Which term in the following inequality is a letter coefficient? Bx+72<12
Responses
72
72
B
upper B
Bx
upper B x
x
Responses
72
72
B
upper B
Bx
upper B x
x
Answered by
GPT 3.5
To solve the inequality Rx > 10, where R is a number greater than 0, we need to isolate the variable x.
Divide both sides of the inequality by R:
(Rx)/R > 10/R
Simplify:
x > 10/R
So, the solution to the inequality Rx > 10, where R is a number greater than 0, is x > 10/R.
Divide both sides of the inequality by R:
(Rx)/R > 10/R
Simplify:
x > 10/R
So, the solution to the inequality Rx > 10, where R is a number greater than 0, is x > 10/R.
Answered by
GPT 3.5
To solve the inequality Ay + 3 < 12, where A is a number greater than 0, we need to isolate the variable y.
Subtract 3 from both sides of the inequality:
Ay + 3 - 3 < 12 - 3
Simplify:
Ay < 9
Divide both sides of the inequality by A:
(Ay)/A < 9/A
Simplify:
y < 9/A
So, the solution to the inequality Ay + 3 < 12, where A is a number greater than 0, is y < 9/A.
Subtract 3 from both sides of the inequality:
Ay + 3 - 3 < 12 - 3
Simplify:
Ay < 9
Divide both sides of the inequality by A:
(Ay)/A < 9/A
Simplify:
y < 9/A
So, the solution to the inequality Ay + 3 < 12, where A is a number greater than 0, is y < 9/A.
Answered by
GPT 3.5
The correct linear inequality that would best translate the problem is: 950 + 25x ≥ 1,700; at least 30 hours
This is because Jorelle needs to have enough money for the trip, which costs $1,300. He currently has $950 in savings and can earn $25 per hour from his online tutoring services. In order to make enough money for the trip, the total amount he earns (25x) added to his savings (950) must be greater than or equal to the total cost of the trip (1,700).
Simplifying the inequality, we have:
950 + 25x ≥ 1,700
To determine the minimum number of hours Jorelle must tutor so he can have enough money for the trip, we solve for x:
25x ≥ 1,700 - 950
25x ≥ 750
x ≥ 30
Therefore, Jorelle must tutor at least 30 hours in order to have enough money for the trip.
This is because Jorelle needs to have enough money for the trip, which costs $1,300. He currently has $950 in savings and can earn $25 per hour from his online tutoring services. In order to make enough money for the trip, the total amount he earns (25x) added to his savings (950) must be greater than or equal to the total cost of the trip (1,700).
Simplifying the inequality, we have:
950 + 25x ≥ 1,700
To determine the minimum number of hours Jorelle must tutor so he can have enough money for the trip, we solve for x:
25x ≥ 1,700 - 950
25x ≥ 750
x ≥ 30
Therefore, Jorelle must tutor at least 30 hours in order to have enough money for the trip.
Answered by
GPT 3.5
The correct step that Mary Ann takes to find the solution set for the inequality −3x ≥ 12 is:
Mary Ann divides both sides of the inequality by −3 and changes the inequality symbol to ≤ to get x ≤ 9.
This step is correct because when dividing by a negative number, the direction of the inequality is reversed. So, by dividing both sides by −3, the inequality symbol changes from ≥ to ≤. And the resulting inequality x ≤ 9 represents the solution set.
Mary Ann divides both sides of the inequality by −3 and changes the inequality symbol to ≤ to get x ≤ 9.
This step is correct because when dividing by a negative number, the direction of the inequality is reversed. So, by dividing both sides by −3, the inequality symbol changes from ≥ to ≤. And the resulting inequality x ≤ 9 represents the solution set.
Answered by
GPT 3.5
The correct way to solve the linear inequality with a letter coefficient Hy < 7, where H is a number greater than 0, is:
y < 7/H
This way, when we divide both sides of the inequality by H, we get the correct solution. Therefore, the correct response is:
y < 7/H
y < 7/H
This way, when we divide both sides of the inequality by H, we get the correct solution. Therefore, the correct response is:
y < 7/H
Answered by
GPT 3.5
The letter coefficient in the inequality Bx + 72 < 12 is:
B
B
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