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.(1 point)
Responses
950+25x≤1,300; at most 14 hours
950 plus 25 x less-than-or-equal-to 1,300 ; at most 14 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 least 30 hours
950 plus 25 x greater-than-or-equal-to 1,700 ; at least 30 hours
950+25x≤1,700; at most 30 hours
950 + 25x ≥ 1,300; at least 14 hours.
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 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 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 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 and changes the inequality symbol to ≤ to get x≤−4.
Mary Ann divides both sides of the inequality by −3 to get x ≤ −4.
Kirk solves the inequality 5<12y−7. Which statement explains the steps he uses to find the solution set of the inequality?(1 point)
Responses
Kirk adds 7 to both sides of the inequality and then multiplies both sides of the equivalent inequality by 12 to get 144<y.
Kirk adds 7 to both sides of the inequality and then multiplies both sides of the equivalent inequality by 12 to get 144 less than y .
Kirk adds 7 to both sides of the inequality and then divides both sides of the equivalent inequality by 12 to get 1<y.
Kirk adds 7 to both sides of the inequality and then divides both sides of the equivalent inequality by 12 to get 1 less than y .
Kirk adds 7 to both sides of the inequality, then divides both sides of the equivalent inequality by 12 and reverses the inequality symbol to get 1>y.
Kirk adds 7 to both sides of the inequality, then divides both sides of the equivalent inequality by 12 and reverses the inequality symbol to get 1 greater than y .
Kirk adds −7 to both sides of the inequality and then divides both sides of the equivalent inequality by 12 to get (−16)<y.
Kirk adds 7 to both sides of the inequality and then divides both sides of the equivalent inequality by 12 to get 1 < y.
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?(1 point)
Responses
y<7H
y less than 7 upper H
Hy<7
upper H y less than 7
y<7
y less than 7
y<7H
y < 7/H
Which term in the following inequality is a letter coefficient? Bx+72<12(1 point)
Responses
x
x
72
72
B
upper B
Bx
B
To determine the minimum number of hours Jorelle must tutor, we need to calculate the total amount of money he has and compare it to the cost of the trip.
Jorelle has $950.00 in savings and earns $25.00 per hour from his online tutoring services. Let's assume he tutors for "x" hours.
To calculate the money he earns from tutoring, we multiply his hourly rate by the number of hours: 25x.
The total amount of money he has is the sum of his savings and tutoring earnings: 950 + 25x.
The trip will cost him $1,300.00.
Now, we need to create a linear inequality using the information above.
Since Jorelle needs to have enough money for the trip, the total amount of money he has (950 + 25x) must be greater than or equal to the cost of the trip ($1,300.00).
Therefore, the linear inequality that best translates the problem is:
950 + 25x ≥ 1,300;
This inequality states that the total amount of money Jorelle has must be greater than or equal to $1,300.00.
To determine the minimum number of hours Jorelle must tutor, we need to solve this inequality:
950 + 25x ≥ 1,300;
Subtract 950 from both sides of the inequality:
25x ≥ 350;
Divide both sides by 25:
x ≥ 14;
Therefore, Jorelle must tutor for at least 14 hours in order to have enough money for the trip.
So, the correct answer is:
950+25x≥1,300; at least 14 hours