To solve the inequality 12-6x>24, we can start by subtracting 12 from both sides to isolate the variable:
-6x > 24 - 12
-6x > 12
Next, divide both sides by -6. However, when dividing an inequality by a negative number, we need to reverse the direction of the inequality sign:
x < 12/-6
x < -2
Therefore, the solution set for the inequality 12-6x>24 is x < -2.
What is the solution set for 12−6x>24 ?(1 point)
Responses
x>2x is greater than 2
x<2x<2
x>−2x is greater than negative 2
x<−2x<−2
11 answers
Our middle school is having a fall carnival. Admission into the carnival is $3 and each game inside the carnival costs $.25. Write an inequality that represents the possible number of games that can be played having $10. What is the maximum number of games that can be played?(1 point)
Responses
0.25x+3≤10; 28 games
0 point 2 5 x plus 3 is less than or equal to 10; 28 games
0.25x−3≤10; 52 games
0 point 2 5 x minus 3 is less than or equal to 10; 52 games
0.25x−3<10; 52 games
0.25x−3<10; 52 games
0.25x+3<10; 28 games
Responses
0.25x+3≤10; 28 games
0 point 2 5 x plus 3 is less than or equal to 10; 28 games
0.25x−3≤10; 52 games
0 point 2 5 x minus 3 is less than or equal to 10; 52 games
0.25x−3<10; 52 games
0.25x−3<10; 52 games
0.25x+3<10; 28 games
To find the maximum number of games that can be played with $10, we need to set up an inequality. Let's call the number of games x.
Each game costs $0.25, so the total cost of the games will be 0.25x.
In addition to the cost of the games, there is also an admission fee of $3.
The total amount spent on the carnival cannot exceed $10, so we can set up the following inequality:
0.25x + 3 ≤ 10
This inequality states that the total cost of the games (0.25x) plus the admission fee (3) is less than or equal to 10.
To find the maximum number of games, we need to solve this inequality. By subtracting 3 from both sides and dividing by 0.25, we can isolate x:
0.25x + 3 - 3 ≤ 10 - 3
0.25x ≤ 7
x ≤ 28
Therefore, the maximum number of games that can be played with $10 is 28 games.
So the correct answer is:
0.25x + 3 ≤ 10; 28 games
Each game costs $0.25, so the total cost of the games will be 0.25x.
In addition to the cost of the games, there is also an admission fee of $3.
The total amount spent on the carnival cannot exceed $10, so we can set up the following inequality:
0.25x + 3 ≤ 10
This inequality states that the total cost of the games (0.25x) plus the admission fee (3) is less than or equal to 10.
To find the maximum number of games, we need to solve this inequality. By subtracting 3 from both sides and dividing by 0.25, we can isolate x:
0.25x + 3 - 3 ≤ 10 - 3
0.25x ≤ 7
x ≤ 28
Therefore, the maximum number of games that can be played with $10 is 28 games.
So the correct answer is:
0.25x + 3 ≤ 10; 28 games
Question
An SAT tutoring service charges a $500 fee for two sessions, plus $50 for each additional session. Emily doesn't want to spend more than $700 on tutoring. What is the maximum number of additional sessions (beyond the first two) that Emily can book for her tutoring sessions?(1 point)
Responses
4
4
5
5
6
6
7
An SAT tutoring service charges a $500 fee for two sessions, plus $50 for each additional session. Emily doesn't want to spend more than $700 on tutoring. What is the maximum number of additional sessions (beyond the first two) that Emily can book for her tutoring sessions?(1 point)
Responses
4
4
5
5
6
6
7
To find the maximum number of additional sessions that Emily can book for her tutoring sessions, we need to set up an inequality.
Let's call the number of additional sessions x.
The cost of the two initial sessions is $500. For each additional session, the cost is $50. Therefore, the total cost for all the sessions can be represented as:
Cost = $500 + $50*x
Emily doesn't want to spend more than $700. So we can set up the following inequality:
$500 + $50*x ≤ $700
To find the maximum number of additional sessions, we need to solve this inequality. By subtracting $500 from both sides and dividing by $50, we can isolate x:
$50*x ≤ $700 - $500
$50*x ≤ $200
x ≤ 4
Therefore, the maximum number of additional sessions that Emily can book for her tutoring sessions is 4.
So the correct answer is:
4
Let's call the number of additional sessions x.
The cost of the two initial sessions is $500. For each additional session, the cost is $50. Therefore, the total cost for all the sessions can be represented as:
Cost = $500 + $50*x
Emily doesn't want to spend more than $700. So we can set up the following inequality:
$500 + $50*x ≤ $700
To find the maximum number of additional sessions, we need to solve this inequality. By subtracting $500 from both sides and dividing by $50, we can isolate x:
$50*x ≤ $700 - $500
$50*x ≤ $200
x ≤ 4
Therefore, the maximum number of additional sessions that Emily can book for her tutoring sessions is 4.
So the correct answer is:
4
Ashley and Liam both have playlists on their music apps.
The number of playlists on Ashley’s app can be represented by X.
The number of playlists on Liam’s app is 4 times the number of playlists on Ashley’s app.
The total number of playlists on both their apps is at least 45.
What is the solution set for x, representing the number of playlists on Ashley’s app?
(1 point)
Responses
x≤−9x is less than or equal to negative 9
x≥−9x is greater than or equal to negative 9
x≥9x is greater than or equal to 9
x≤9
The number of playlists on Ashley’s app can be represented by X.
The number of playlists on Liam’s app is 4 times the number of playlists on Ashley’s app.
The total number of playlists on both their apps is at least 45.
What is the solution set for x, representing the number of playlists on Ashley’s app?
(1 point)
Responses
x≤−9x is less than or equal to negative 9
x≥−9x is greater than or equal to negative 9
x≥9x is greater than or equal to 9
x≤9
Let's represent the number of playlists on Ashley's app as x.
According to the given information, the number of playlists on Liam's app is 4 times the number of playlists on Ashley's app. This can be written as 4x.
The total number of playlists on both their apps is at least 45, so we can set up the following inequality:
x + 4x ≥ 45
Combining like terms, we have:
5x ≥ 45
To isolate x, we divide both sides of the inequality by 5:
x ≥ 45/5
x ≥ 9
Therefore, the solution set for x, representing the number of playlists on Ashley's app, is x ≥ 9.
So the correct answer is:
x ≥ 9
According to the given information, the number of playlists on Liam's app is 4 times the number of playlists on Ashley's app. This can be written as 4x.
The total number of playlists on both their apps is at least 45, so we can set up the following inequality:
x + 4x ≥ 45
Combining like terms, we have:
5x ≥ 45
To isolate x, we divide both sides of the inequality by 5:
x ≥ 45/5
x ≥ 9
Therefore, the solution set for x, representing the number of playlists on Ashley's app, is x ≥ 9.
So the correct answer is:
x ≥ 9
Olivia visited a stationery shop to buy journals.
She had $36 allocated for the purchase.
Olivia bought 4 journals.
Following the purchase, Olivia had less than $12 remaining.
What is the solution set for x, representing the cost of each journal?
(1 point)
Responses
x>$3x is greater than 3 dollars
x>$4x is greater than 4 dollars
x>$5x is greater than 5 dollars
x>$6
She had $36 allocated for the purchase.
Olivia bought 4 journals.
Following the purchase, Olivia had less than $12 remaining.
What is the solution set for x, representing the cost of each journal?
(1 point)
Responses
x>$3x is greater than 3 dollars
x>$4x is greater than 4 dollars
x>$5x is greater than 5 dollars
x>$6
Let's represent the cost of each journal as x.
According to the given information, Olivia had $36 allocated for the purchase, and she bought 4 journals. This means she spent a total of 4x dollars on the journals.
After the purchase, Olivia had less than $12 remaining. This can be written as:
36 - 4x < 12
To find the solution set for x, we can solve this inequality. By subtracting 36 from both sides, we have:
-4x < 12 - 36
-4x < -24
Dividing both sides of the inequality by -4, we need to reverse the direction of the inequality sign:
x > -24 / -4
x > 6
Therefore, the solution set for x, representing the cost of each journal, is x > 6.
So the correct answer is:
x > 6
According to the given information, Olivia had $36 allocated for the purchase, and she bought 4 journals. This means she spent a total of 4x dollars on the journals.
After the purchase, Olivia had less than $12 remaining. This can be written as:
36 - 4x < 12
To find the solution set for x, we can solve this inequality. By subtracting 36 from both sides, we have:
-4x < 12 - 36
-4x < -24
Dividing both sides of the inequality by -4, we need to reverse the direction of the inequality sign:
x > -24 / -4
x > 6
Therefore, the solution set for x, representing the cost of each journal, is x > 6.
So the correct answer is:
x > 6
Preston solved the inequality and graphed it on the number line. Which of the following is the inequality that he solved?
(1 point)
Responses
2.1x+5.6≥8.752 point 1 x plus 5 point 6 is greater than or equal to 8 point 7 5
0.9x+2.8≤5.950 point 9 x plus 2 point 8 is less than or equal to 5 point 9 5
5.6x−18.9≤0.75 point 6 x minus 18 point 9 is less than or equal to 0 point 7
3.4x−1.2≥4.75
(1 point)
Responses
2.1x+5.6≥8.752 point 1 x plus 5 point 6 is greater than or equal to 8 point 7 5
0.9x+2.8≤5.950 point 9 x plus 2 point 8 is less than or equal to 5 point 9 5
5.6x−18.9≤0.75 point 6 x minus 18 point 9 is less than or equal to 0 point 7
3.4x−1.2≥4.75
Based on the given options, it is not possible to determine the exact inequality that Preston solved without further information. None of the options listed above match the provided inequality or have the same structure.
3 answers