orelle 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)

Question

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≤1,300; 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

Answer 1

To determine how much money Jorelle needs for his trip, let's break down the costs:

1. The total cost for airfare, food, and itineraries is $1,300.
2. Jorelle will stay in a hotel for 5 nights at $80 per night. Therefore, the total cost for the hotel is: \[ 5 \text{ nights} \times 80 \text{ dollars/night} = 400 \text{ dollars} \]
3. The total amount Jorelle needs for the trip is: \[ 1,300 \text{ dollars} + 400 \text{ dollars} = 1,700 \text{ dollars} \]

Now, let's denote \( x \) as the number of hours Jorelle tutors. He earns $25 per hour. Therefore, the amount of money he will earn from tutoring is \( 25x \).

Jorelle currently has $950 in savings. The total amount of money he will have after tutoring is: \[ 950 + 25x \]

To ensure he has enough money for the trip, we can set up the following linear inequality: \[ 950 + 25x \geq 1,700 \]

Now, to find the minimum number of hours he must tutor, we solve the inequality: \[ 25x \geq 1,700 - 950 \] \[ 25x \geq 750 \] \[ x \geq \frac{750}{25} \] \[ x \geq 30 \]

So, Jorelle must tutor at least 30 hours to have enough money for the trip.

Thus, the correct response is: 950 + 25x ≥ 1,700; at least 30 hours.

Answer 2

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 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 and changes the inequality symbol to ≤ to get x≤9.

Answer 3

Let's analyze Mary Ann's steps for solving the inequality \( -3x \geq 12 \).

1. First Step: To isolate \( x \), Mary Ann needs to divide both sides of the inequality by \( -3 \). In solving inequalities, when we divide or multiply by a negative number, we must reverse the inequality sign.

2. Applying the Step: Thus, when Mary Ann divides both sides of the inequality by \( -3 \), the inequality will change from \( \geq \) to \( \leq \).

So starting with: \[ -3x \geq 12 \] After dividing both sides by \( -3 \): \[ x \leq \frac{12}{-3} \] This simplifies to: \[ x \leq -4 \]

Therefore, the correct justification for Mary Ann's steps is: Mary Ann divides both sides of the inequality by −3 and changes the inequality symbol to ≤ to get x ≤ −4.

Answer 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 (−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.
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.

Answer 5

To solve the inequality \( 5 < 12y - 7 \), let's break down Kirk's steps clearly:

1. Starting Inequality: \[ 5 < 12y - 7 \]

2. Step 1: Add \( 7 \) to both sides of the inequality to isolate the term with \( y \): \[ 5 + 7 < 12y \] This simplifies to: \[ 12 < 12y \]

3. Step 2: Divide both sides of the inequality by \( 12 \): \[ \frac{12}{12} < y \] This simplifies to: \[ 1 < y \]

Thus, the final solution can also be written as: \[ y > 1 \]

The correct option that explains Kirk's steps 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.

Answer 6

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

Hy<7
upper H y less than 7

y<7H
y less than Start Fraction 7 over upper H End Fraction

y<7H
y less than 7 upper H

y<7

Answer 7

To solve the linear inequality \( Hy < 7 \) where \( H \) is a number greater than \( 0 \), we would want to isolate \( y \) on one side. Since \( H \) is positive, we can divide both sides of the inequality by \( H \) without reversing the inequality sign.

Starting with the inequality: \[ Hy < 7 \]

Next, divide both sides by \( H \): \[ y < \frac{7}{H} \]

So, the way to express the solution is: \( y < \frac{7}{H} \)

Thus, the correct response is: y < 7H (where H is a coefficient on y) is not correct, but y < \frac{7}{H} is what we derived. However, if the exact formulation "Start Fraction 7 over upper H End Fraction" correctly conveys that division, it should correspond to the value \( y < \frac{7}{H} \).

Since "y < 7H" and "y < 7" do not represent the solution, make sure to identify which phrase correctly indicates the division by \( H \). If that choice is given as: y < Start Fraction 7 over upper H End Fraction, that would be the accurate representation.

If you have the option that shows \( y < \frac{7}{H} \), select that.

Answer 8

Which term in the following inequality is a letter coefficient? Bx+72<12(1 point)
Responses

Bx
upper B x

x
x

72
72

B

Answer 9

In the inequality \( Bx + 72 < 12 \), the term that contains a letter coefficient is \( Bx \). In this expression, \( B \) is the letter coefficient (the coefficient of \( x \)), and \( x \) is the variable.

To clarify:

• \( Bx \) refers to the entire term where \( B \) is the coefficient of the variable \( x \).
• \( 72 \) is a constant.
• \( x \) is the variable.
• \( B \) by itself is just the coefficient.

Given your response options, the one that clearly indicates the term with the letter coefficient is:

Bx (or upper B x).

So the correct answer is: Bx