To solve the inequality 6x+1<5x-8, we can start by subtracting 5x from both sides:
6x + 1 - 5x < 5x - 8 - 5x
x + 1 < -8
Next, we can subtract 1 from both sides:
x + 1 - 1 < -8 - 1
x < -9
Solve the inequality 6x+1<5x−8.
19 answers
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?
Let's assume that Shantel works x hours each month.
Her monthly earnings from tutoring would be 25x dollars.
Her monthly expenses are $3,200.
Shantel's profit would be the difference between her earnings and expenses, which is given by:
Profit = Earnings - Expenses
Profit = 25x - 3200
We want Shantel's profit to be at least $600, so we can set up the inequality:
25x - 3200 ≥ 600
Adding 3200 to both sides of the inequality, we get:
25x ≥ 3800
Dividing both sides of the inequality by 25, we get:
x ≥ 152
Therefore, Shantel must work at least 152 hours each month to earn a monthly profit of at least $600.
Her monthly earnings from tutoring would be 25x dollars.
Her monthly expenses are $3,200.
Shantel's profit would be the difference between her earnings and expenses, which is given by:
Profit = Earnings - Expenses
Profit = 25x - 3200
We want Shantel's profit to be at least $600, so we can set up the inequality:
25x - 3200 ≥ 600
Adding 3200 to both sides of the inequality, we get:
25x ≥ 3800
Dividing both sides of the inequality by 25, we get:
x ≥ 152
Therefore, Shantel must work at least 152 hours each month to earn a monthly profit of at least $600.
La’Shondra solves the inequality 6+3x≤24. She begins by subtracting 6 from both sides of the inequality and then divides both sides of the equivalent inequality by a number. What is the number?
To solve the inequality 6 + 3x ≤ 24, La'Shondra begins by subtracting 6 from both sides of the inequality:
6 + 3x - 6 ≤ 24 - 6
This simplifies to:
3x ≤ 18
La'Shondra then divides both sides of the inequality by a number to solve for x.
To determine the number, we need to divide by the coefficient of x, which is 3.
Dividing both sides of the inequality by 3:
(3x)/3 ≤ 18/3
This simplifies to:
x ≤ 6
Therefore, the number La'Shondra divided both sides of the inequality by is 3.
6 + 3x - 6 ≤ 24 - 6
This simplifies to:
3x ≤ 18
La'Shondra then divides both sides of the inequality by a number to solve for x.
To determine the number, we need to divide by the coefficient of x, which is 3.
Dividing both sides of the inequality by 3:
(3x)/3 ≤ 18/3
This simplifies to:
x ≤ 6
Therefore, the number La'Shondra divided both sides of the inequality by is 3.
Solve the inequality Rx>10, where R is a number greater than 0.
To solve the inequality Rx > 10, we need to divide both sides of the inequality by R.
However, since we don't know the value of R, we cannot divide both sides by it.
We do know that R is a number greater than 0, which means it's a positive number.
Therefore, to isolate x, we can divide both sides of the inequality by a positive number greater than 0.
In this case, we can divide both sides by a positive constant, let's say C, where C is greater than 0.
Dividing both sides by C:
(Rx) / C > 10 / C
Simplifying this expression, we get:
x > (10 / C)
So, the inequality Rx > 10 can be written as x > (10 / C), where C is any positive number greater than 0.
However, since we don't know the value of R, we cannot divide both sides by it.
We do know that R is a number greater than 0, which means it's a positive number.
Therefore, to isolate x, we can divide both sides of the inequality by a positive number greater than 0.
In this case, we can divide both sides by a positive constant, let's say C, where C is greater than 0.
Dividing both sides by C:
(Rx) / C > 10 / C
Simplifying this expression, we get:
x > (10 / C)
So, the inequality Rx > 10 can be written as x > (10 / C), where C is any positive number greater than 0.
Solve the inequality Ay+3<12, where A is a number greater than 0.
To solve the inequality Ay + 3 < 12, we will subtract 3 from both sides of the inequality.
Ay < 12 - 3
Simplifying, we get:
Ay < 9
To isolate y, we can divide both sides of the inequality by A. Since A is a number greater than 0, we can divide by A without changing the direction of the inequality.
(Ay) / A < 9 / A
This simplifies to:
y < 9/A
So, the solution to the inequality Ay + 3 < 12, where A is a number greater than 0, is y < 9/A, where A is any positive number greater than 0.
Ay < 12 - 3
Simplifying, we get:
Ay < 9
To isolate y, we can divide both sides of the inequality by A. Since A is a number greater than 0, we can divide by A without changing the direction of the inequality.
(Ay) / A < 9 / A
This simplifies to:
y < 9/A
So, the solution to the inequality Ay + 3 < 12, where A is a number greater than 0, is y < 9/A, where A is any positive number greater than 0.
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
A) 950+25x≤1,700; at most 30 hours
B) 950+25x≤1,300; at most 14 hours
C)950+25x≥1,300; at least 14 hours
D) 950+25x≥1,700; at least 30 hours
Responses
A) 950+25x≤1,700; at most 30 hours
B) 950+25x≤1,300; at most 14 hours
C)950+25x≥1,300; at least 14 hours
D) 950+25x≥1,700; at least 30 hours
The total cost of Jorelle's trip is $1,300, and he only has $950 in savings.
To determine the minimum number of tutoring hours Jorelle must work to have enough money for the trip, we need to find an inequality that represents the total amount of money he will have after tutoring.
Jorelle earns $25 per hour, so if he works x hours, his earnings from tutoring will be 25x.
After working those hours, he will have $950 + 25x.
To ensure that he has enough money for the trip, the total amount of money he will have after tutoring should be equal to or greater than the total cost of the trip.
Therefore, the correct inequality is:
950 + 25x ≥ 1,300.
This means that Jorelle must tutor for at least 14 hours (Choice C) in order to have enough money for the trip.
To determine the minimum number of tutoring hours Jorelle must work to have enough money for the trip, we need to find an inequality that represents the total amount of money he will have after tutoring.
Jorelle earns $25 per hour, so if he works x hours, his earnings from tutoring will be 25x.
After working those hours, he will have $950 + 25x.
To ensure that he has enough money for the trip, the total amount of money he will have after tutoring should be equal to or greater than the total cost of the trip.
Therefore, the correct inequality is:
950 + 25x ≥ 1,300.
This means that Jorelle must tutor for at least 14 hours (Choice C) in order to have enough money for the trip.
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 and changes the inequality symbol to ≤ to get x≤9.
C) Mary Ann divides both sides of the inequality by −3 and changes the inequality symbol to ≤ to get x≤−4.
D) Mary Ann adds −3 to both sides of the inequality to get x≥9.
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 and changes the inequality symbol to ≤ to get x≤9.
C) Mary Ann divides both sides of the inequality by −3 and changes the inequality symbol to ≤ to get x≤−4.
D) Mary Ann adds −3 to both sides of the inequality to get x≥9.
To solve the inequality -3x ≥ 12, Mary Ann correctly divides both sides of the inequality by -3.
However, when dividing both sides of an inequality by a negative number, the inequality symbol needs to be flipped.
Therefore, the correct step Mary Ann takes is:
Mary Ann divides both sides of the inequality by -3 and changes the inequality symbol to ≤, which gives x ≤ -4.
So, the correct answer is Choice C: Mary Ann divides both sides of the inequality by -3 and changes the inequality symbol to ≤ to get x ≤ -4.
However, when dividing both sides of an inequality by a negative number, the inequality symbol needs to be flipped.
Therefore, the correct step Mary Ann takes is:
Mary Ann divides both sides of the inequality by -3 and changes the inequality symbol to ≤, which gives x ≤ -4.
So, the correct answer is Choice C: Mary Ann divides both sides of the inequality by -3 and changes the inequality symbol to ≤ to get x ≤ -4.
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
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 divides both sides of the equivalent inequality by 12 to get 1<y.
C) Kirk adds 7 to both sides of the inequality and then multiplies both sides of the equivalent inequality by 12 to get 144<y.
D) Kirk adds −7 to both sides of the inequality and then divides both sides of the equivalent inequality by 12 to get (−16)<y.
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
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 divides both sides of the equivalent inequality by 12 to get 1<y.
C) Kirk adds 7 to both sides of the inequality and then multiplies both sides of the equivalent inequality by 12 to get 144<y.
D) Kirk adds −7 to both sides of the inequality and then divides both sides of the equivalent inequality by 12 to get (−16)<y.
To solve the inequality 5 < 12y - 7, Kirk adds 7 to both sides of the inequality.
This gives us 5 + 7 < 12y - 7 + 7, which simplifies to 12 < 12y.
Next, Kirk divides both sides of the inequality by 12.
Dividing both sides by 12, we get (12/12) < (12y/12), which simplifies to 1 < y.
Therefore, the correct steps Kirk uses to find the solution set of the inequality are:
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 answer is Choice B: Kirk adds 7 to both sides of the inequality and then divides both sides of the equivalent inequality by 12 to get 1 < y.
This gives us 5 + 7 < 12y - 7 + 7, which simplifies to 12 < 12y.
Next, Kirk divides both sides of the inequality by 12.
Dividing both sides by 12, we get (12/12) < (12y/12), which simplifies to 1 < y.
Therefore, the correct steps Kirk uses to find the solution set of the inequality are:
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 answer is Choice B: 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) Hy<7
B) y<7
C) y<7H
D) y<7H
Responses
A) Hy<7
B) y<7
C) y<7H
D) y<7H
To solve the linear inequality Hy < 7, where H is a number greater than 0, we need to isolate the variable y by dividing both sides of the inequality by H.
Dividing both sides by H, we get:
Hy / H < 7 / H
Simplifying, we have:
y < 7/H
Therefore, the correct answer is Choice C: y < 7H.
Dividing both sides by H, we get:
Hy / H < 7 / H
Simplifying, we have:
y < 7/H
Therefore, the correct answer is Choice C: y < 7H.
Which term in the following inequality is a letter coefficient? Bx+72<12(1 point)
Responses
A) B
B) x
C) 72
D) Bx
Responses
A) B
B) x
C) 72
D) Bx
In the inequality Bx + 72 < 12, the term Bx has a letter coefficient.
Therefore, the correct answer is Choice D: Bx.
Therefore, the correct answer is Choice D: Bx.