Question

Solve the inequality 6x+1<5x−8.(1 point)
Answer
Shantel offers online tutorial services. She charges $25.00 an hour per student. Her budget tracker reflects a total of $3,200.00 monthly expenses. How many hours must Shantel work each month to earn a monthly profit of at least $600.00?(1 point)
at least
hours
Answer
Solve the inequality Ay+3<12, where A is a number greater than 0.(1 point)
Answer

Solve Linear Inequalities Quick Check
1 of 51 of 5 Items
Question
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 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 plus 25 x less-than-or-equal-to 1,700 ; at most 30 hours

950+25x≥1,300; at least 14 hours
Answer

Solve Linear Inequalities Quick Check
2 of 52 of 5 Items
Question
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 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.
Mary Ann adds negative 3 to both sides of the inequality to get x greater-than-or-equal-to 9 .

Mary Ann adds −3 to both sides of the inequality and changes the inequality symbol to ≤ to get x≤9.
Answer

Solve Linear Inequalities Quick Check
3 of 53 of 5 Items
Question
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
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?(1 point)
Responses

y<7
y less than 7

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

Hy<7
upper H y less than 7

y<7H
Answer

Solve Linear Inequalities Quick Check
5 of 55 of 5 Items
Question
Which term in the following inequality is a letter coefficient? Bx+72<12(1 point)
Responses

72
72

Bx
upper B x

B
upper B

x
Answered by GPT 3.5
To solve the inequality, we need to isolate the variable x on one side.

First, let's get rid of the x term on the right side by subtracting 5x from both sides:

6x + 1 - 5x < 5x - 8 - 5x

Simplifying this, we get:

x + 1 < -8

Next, let's isolate x by subtracting 1 from both sides:

x + 1 - 1 < -8 - 1

Simplifying further, we get:

x < -9

So the solution to the inequality is x < -9.
Answered by GPT 3.5
Let's denote the number of hours Shantel must work each month as x.

Shantel earns $25.00 per hour, so her monthly earnings can be represented as 25x.

Her monthly expenses are $3,200.00.

To calculate her monthly profit, we subtract her expenses from her earnings:

Profit = Earnings - Expenses

Profit = 25x - 3200

We want to find the minimum number of hours Shantel needs to work to earn a profit of at least $600.00. In other words, we want to find the value of x that satisfies the inequality:

25x - 3200 ≥ 600

To solve this inequality, we need to isolate the variable x on one side. Let's add 3200 to both sides:

25x - 3200 + 3200 ≥ 600 + 3200

Simplifying:

25x ≥ 3800

Next, divide both sides of the inequality by 25 to isolate x:

25x/25 ≥ 3800/25

Simplifying:

x ≥ 152

Therefore, Shantel must work at least 152 hours each month to earn a monthly profit of at least $600.00.
Answered by GPT 3.5
To solve the inequality Ay + 3 < 12, we need to isolate the variable y on one side.

First, let's subtract 3 from both sides:

Ay + 3 - 3 < 12 - 3

This simplifies to:

Ay < 9

Next, to isolate y, we divide both sides by A:

(Ay)/A < 9/A

The A term on the left side cancels out, and we are left with:

y < 9/A

Since A is a number greater than 0, we know that 9/A is a positive number. Therefore, we can write the solution as:

y < 9/A
Answered by GPT 3.5
The correct linear inequality that best translates the problem is:

950 + 25x ≥ 1,300; at least 14 hours

This inequality represents the minimum amount of tutoring hours Jorelle must work in order to have enough money for the trip.
Answered by GPT 3.5
The correct steps that Mary Ann takes to find the solution set for the inequality -3x ≥ 12 are:

1. Mary Ann divides both sides of the inequality by -3 to get x ≤ -4.
2. Mary Ann changes the inequality symbol to ≤ because dividing by a negative number flips the inequality.

So, the correct response is:

Mary Ann divides both sides of the inequality by -3 and changes the inequality symbol to ≤ to get x ≤ -4.
Answered by GPT 3.5
The correct statement explaining the steps Kirk uses to find the solution set of the inequality 5 < 12y - 7 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.

So, the correct response 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.
Answered by GPT 3.5
The correct way to solve the linear inequality "Hy < 7" is:

y < 7/H

So, the correct response is:

y < 7/H
Answered by GPT 3.5
The term in the inequality "Bx + 72 < 12" that is a letter coefficient is:

Bx

So, the correct response is:

Bx