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.
A. 950 + 25x ≤ 1,700; at most 30 hours
B. 950 + 25x ≥ 1,700; at least 30 hours
C. 950 + 25x ≥ 1,300; at least 14 hours
D. 950 + 25x ≤ 1,300; at most 14 hours
The correct linear inequality to represent the problem is:
950 + 25x ≥ 1,300; at least 14 hours
Explanation:
The total cost of the trip is $1,300. Jorelle has $950 in savings, so he needs to earn the remaining amount. He earns $25 per hour from his online tutoring services, so the minimum number of hours he must tutor can be found by subtracting his savings from the total costs and dividing by his hourly rate:
1,300 - 950 = 350
350 / 25 = 14
Therefore, Jorelle must tutor at least 14 hours to have enough money for the trip.
The correct step that Mary Ann takes to find the solution set to the inequality −3x ≥ 12 is:
D. Mary Ann divides both sides of the inequality by −3 and changes the inequality symbol to ≤ to get x≤−4.
Explanation:
To solve the inequality, Mary Ann needs to isolate the variable x. She can do this by dividing both sides of the inequality by -3. However, when dividing by a negative number, the inequality symbol needs to be flipped. So, the inequality −3x ≥ 12 becomes x ≤ -4 when divided by -3.
The correct statement that explains the steps Kirk uses to find the solution set of the inequality 5 < 12y - 7 is:
D. Kirk adds 7 to both sides of the inequality and then divides both sides of the equivalent inequality by 12 to get 1 < y.
Explanation:
To solve the inequality, Kirk first adds 7 to both sides of the inequality to get 5 + 7 < 12y - 7 + 7, which simplifies to 12 < 12y. Then, he divides both sides of the inequality by 12 to get 12/12 < 12y/12, or 1 < y. Therefore, the solution set of the inequality is y > 1.
The correct answer is:
D. y < 7
Explanation:
To solve the linear inequality Hy < 7, where H is a number greater than 0, we divide both sides of the inequality by H. This results in y < 7/H. Since H is greater than 0, the value of 7/H will be positive, and we do not need to include H in the inequality. Therefore, the solution is y < 7.
Mary Ann solves the inequality −3x ≥ 12. Justify the steps Mary Ann takes to find the solution set.(1 point)
Responses
A. Mary Ann divides both sides of the inequality by −3 to get x≥−4.
B. Mary Ann adds −3 to both sides of the inequality to get x≥9.
C. Mary Ann adds −3 to both sides of the inequality and changes the inequality symbol to ≤ to get x ≤ 9.
D. Mary Ann divides both sides of the inequality by −3 and changes the inequality symbol to ≤ 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
A. 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.
B. Kirk adds 7 to both sides of the inequality and then multiplies both sides of the equivalent inequality by 12 to get 144 < y.
C. Kirk adds −7 to both sides of the inequality and then divides both sides of the equivalent inequality by 12 to get (−16) < y.
D. 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
A. y < 7H
B. Hy < 7
C. y < 7H
D. y < 7
Which term in the following inequality is a letter coefficient? Bx + 72 < 12
A. x
B. 72
C. Bx
D. B
The letter coefficient in the inequality Bx + 72 < 12 is:
C. Bx
Explanation:
The term "Bx" includes both the letter "B" and the variable "x". The coefficient of the variable "x" is the letter coefficient in this inequality.