Solve the inequality 6x+1<5x−8.
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
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.
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.
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.
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.
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