Solve for x to determine if the equation has one, none, or infinite solutions.
4x=3(x+5)−15(1 point)
Responses
The equation has no solution.
The equation has no solution.
The equation has infinite solutions.
The equation has infinite solutions.
The equation has one solution: x=0.
The equation has one solution: x equals 0 .
The equation has one solution: x=−10.
The equation has one solution: x equals negative 10 .
To solve the equation 4x = 3(x + 5) - 15, we can start by distributing the 3 on the right side:
4x = 3x + 15 - 15
Simplifying further, we have:
4x = 3x
Now, subtracting 3x from both sides, we get:
x = 0
Therefore, the equation has one solution: x = 0.
Solve for x to determine if the equation has one, none, or infinite solutions.
5(2x+2)−7x=3x+6(1 point)
Responses
The equation has no solution.
The equation has no solution.
The equation has one solution: x=6.
The equation has one solution: x equals 6 .
The equation has infinite solutions.
The equation has infinite solutions.
The equation has one solution: x=10.
To solve the equation 5(2x + 2) - 7x = 3x + 6, we can start by distributing the 5 on the left side:
10x + 10 - 7x = 3x + 6
Combining like terms, we get:
3x + 10 = 3x + 6
Now, subtracting 3x from both sides, we have:
10 = 6
This is a contradiction because 10 is not equal to 6.
Therefore, the equation has no solution.
Solve the inequality 6x+1<5x−8.(1 point)
x
a
To solve the inequality 6x + 1 < 5x - 8, we can start by isolating the x term on one side of the inequality.
Subtracting 5x from both sides, we get:
6x - 5x + 1 < -8
Simplifying further, we have:
x + 1 < -8
Now, subtracting 1 from both sides:
x < -8 - 1
x < -9
Therefore, the solution to the inequality is 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?(1 point)
at least
hours
To determine how many hours Shantel must work each month to earn a monthly profit of at least $600, we need to set up an equation.
Let's let x represent the number of hours Shantel works each month.
She charges $25.00 per hour per student, so her total earnings from tutoring each month can be calculated as 25x.
Her monthly expenses are $3,200.00.
To find the monthly profit, we subtract the expenses from the earnings:
Profit = Earnings - Expenses
Profit = 25x - 3200
We want the profit to be at least $600, so we can set up the following inequality:
25x - 3200 ≥ 600
Adding 3200 to both sides of the inequality, we get:
25x ≥ 3800
Dividing both sides by 25, we find:
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?(1 point)
To solve the inequality 6 + 3x ≤ 24, La'Shondra begins by subtracting 6 from both sides:
6 + 3x - 6 ≤ 24 - 6
Simplifying further:
3x ≤ 18
To isolate x on one side of the inequality, La'Shondra needs to divide both sides by a number. In this case, the number is 3.
Dividing both sides by 3, we get:
(3x) / 3 ≤ 18 / 3
Simplifying:
x ≤ 6
Therefore, the number that La'Shondra divides both sides of the inequality by is 3.
Solve the inequality Rx>10, where R is a number greater than 0.(1 point)
x
over R