Tonisha has a lemonade stand. She has $36 in expenses and wants to make at least $55 per day. If x represents the amount of revenue from selling lemonade, an inequality to represent the amount of revenue she would need to generate would be: (2 points)
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
x
Response area
36
Response area
55
+-<>
≥
≥
≤
The inequality to represent the amount of revenue she would need to generate would be x ≥ 36 + 55.
Tonisha needs to sell (refer back to the previous answer you selected and solve the inequality)(2 points)
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
x
Response area
Response area
><
≤
≤
≥
Tonisha needs to sell at least $91 worth of lemonade.
Lamont has purchased 20 trading cards and wants to have at most 50 trading cards. Write and solve an inequality to find the number of trading cards Lamont needs. Select all of the true statements.(2 points)
Responses
x + 20 ≥ 50
x + 20 ≥ 50
x + 20 ≤ 50
x + 20 ≤ 50
x ≥ 30
x ≥ 30
x ≤ 30
x ≤ 30
x ≥ 70
The correct inequality to find the number of trading cards Lamont needs is x + 20 ≤ 50.
Solving this inequality, we subtract 20 from both sides: x ≤ 50 - 20.
Therefore, Lamont needs x ≤ 30 trading cards.
The true statements are:
- x + 20 ≤ 50
- x ≤ 30
At a campground, kayak rental company A charges a fixed amount of $10 plus $8 per hour for renting a one-person kayak. Company B charges a fixed amount of $6 plus $10 per hour for a one-person kayak. Write and solve an inequality representing the number of hours where Option A will be the cheaper rental company. Let x represent the number of hours.(1 point)
Responses
10 + 8x > 6 + 10x; x < 2
10 + 8x > 6 + 10x; x < 2
6+10x < 10 + 8x; x > 2
6+10x < 10 + 8x; x > 2
10+ 8x < 6 + 10x; x > 2
10+ 8x < 6 + 10x; x > 2
6 + 10 x > 10 + 8x; x < 2
The correct inequality representing the number of hours where Option A will be the cheaper rental company is:
10 + 8x < 6 + 10x
Now, let's solve it:
Subtract 8x from both sides: 10 < 6 + 2x
Subtract 6 from both sides: 4 < 2x
Divide both sides by 2: 2 < x
Therefore, the inequality is: x > 2
The correct response is: 6 + 10x < 10 + 8x; x > 2
Solve and graph the solution to the compound inequality.
−4x ≥ 36 or x − 7 ≥ −3
(1 point)
Responses
x ≤ 5
x ≤ 5
x ≤ -9 or x ≥ 4
x ≤ -9 or x ≥ 4
x ≤ -5 or x > -3
x ≤ -5 or x > -3
x ≥ 4
To solve the compound inequality, we will solve each inequality separately and then combine the solutions.
For the first inequality, −4x ≥ 36, we need to divide both sides by -4. Remember that when we divide or multiply both sides of an inequality by a negative number, we need to reverse the inequality sign.
So we have x ≤ -9.
For the second inequality, x − 7 ≥ −3, we need to add 7 to both sides:
x ≥ 4.
Therefore, the solutions to the compound inequality are x ≤ -9 or x ≥ 4.
The correct response is: x ≤ -9 or x ≥ 4.
Solve and graph the compound inequality on a number line.
x4 < −1 and x + 6 > −2
(1 point)
Responses
x > -6
x > -6
{All Real Numbers}
{All Real Numbers}
-6 < x < 6
-6 < x < 6
-8 < x < -4