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≤1,700; at most 30 hours
950 plus 25 x less-than-or-equal-to 1,700 ; at most 30 hours
950+25x≥1,300; at 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
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The correct answer is:
950+25x≥1,300; at least 14 hours
950 plus 25 x greater-than-or-equal-to 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 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 negative 3 and changes the inequality symbol to less-than-or-equal-to to get x less-than-or-equal-to negative 4 .
Mary Ann adds −3 to both sides of the inequality to get x≥9.
The correct answer is:
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 .
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, 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 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 and then divides both sides of the equivalent inequality by 12 to get (−16)<y.
Kirk adds negative 7 to both sides of the inequality and then divides both sides of the equivalent inequality by 12 to get left parenthesis negative Start Fraction 1 over 6 End Fraction right parenthesis less than y .
Kirk adds 7 to both sides of the inequality and then multiplies both sides of the equivalent inequality by 12 to get 144<y.
The correct answer is:
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
y<7H
y less than Start Fraction 7 over upper H End Fraction
y<7
y less than 7
Hy<7
The correct answer is:
y<7/H
Which term in the following inequality is a letter coefficient? Bx+72<12(1 point)
The term "Bx" is a letter coefficient in the inequality Bx + 72 < 12.
To determine the minimum number of hours Jorelle must tutor in order to have enough money for the trip, we need to create a linear inequality in one variable that represents his savings and earnings.
Let's start by calculating the total cost of the trip. We know that the cost of airfare, food, and itineraries is $1,300.00 and he plans to stay in a hotel room for $80.00 per night. Since the trip is 5 days long, the cost of the hotel room for the entire trip is 5 * $80.00 = $400.00.
The total cost of the trip is then $1,300.00 + $400.00 = $1,700.00.
Now, let's define the variable x to represent the number of hours Jorelle needs to tutor. We also know that he has $950.00 in savings and earns $25.00 per hour from his online tutoring services.
Let's express this situation as a linear inequality:
Jorelle's savings plus (25 * number of hours tutor) should be less than or equal to the total cost of the trip.
950 + 25x ≤ 1,700
Therefore, the linear inequality that best translates the problem is:
950 + 25x ≤ 1,700; at most 30 hours
This inequality states that Jorelle's savings plus 25 times the number of hours he tutors must be less than or equal to $1,700. The solution to this inequality is x ≤ 30, which means that Jorelle must tutor at most 30 hours in order to have enough money for the trip.