Question

Which values are in the solution set of the inequality −2/3x + 13 ≥ −1 ?−23x + 13 ≥ −1 ? Select all that apply. (3 points) Responses 19 19 20 20 21 21 22 22 23

Answer 1

[AI-generated answer — Bot GPT 3.5]

To solve the inequality, we need to isolate the variable x.

−2/3x + 13 ≥ −1

Subtract 13 from both sides:

−2/3x ≥ −1 - 13
−2/3x ≥ -14

To get rid of the fraction, multiply both sides by -3/2 (reciprocal of -2/3):

(-2/3x)(-3/2) ≤ -14(-3/2)
x ≤ 21

Therefore, the solution set is the set of values that are less than or equal to 21. Therefore, the values in the solution set are 19, 20, and 21.

Answer 2

The above compound inequality is true only if _________ of the statement(s) is/are true.(1 point) Responses none none all all at least 1

Answer 3

[AI-generated answer — Bot GPT 3.5]

The above compound inequality is true only if at least 1 of the statement(s) is/are true.

Answer 4

Solve for x. 18 > 2x + 4 ≥ 4 (1 point) Responses 14 < x ≤ 4 14 < x ≤ 4 7 > x > 8 7 > x > 8 7 > x ≥ 12 7 > x ≥ 12 7 > x ≥ 4 7 > x ≥ 4 7 > x ≥ 0

Answer 5

[AI-generated answer — Bot GPT 3.5]

To solve the inequality, we need to isolate the variable x.

Given: 18 > 2x + 4 ≥ 4

Subtract 4 from all sides of the inequality:

14 > 2x ≥ 0

Next, divide all parts of the inequality by 2:

7 > x ≥ 0

So, the solution for x is 7>x≥0.

Answer 6

For which compound inequalities is 6 a solution? Select the statements that are true.(3 points) Responses -5 < x < 6 -5 < x < 6 -2 ≤ x ≤ 6 -2 ≤ x ≤ 6 x ≤ 2 or x ≥ 6 x ≤ 2 or x ≥ 6 x < 2 or x > 6 x < 2 or x > 6 x < -5 or x > 0

Answer 7

[AI-generated answer — Bot GPT 3.5]

To determine if 6 is a solution for each compound inequality, we can substitute 6 into each inequality and see if the statement is true.

-5 < x < 6:
6 does not satisfy this inequality, so it is not a solution.

-2 ≤ x ≤ 6:
6 satisfies this inequality since it is less than or equal to 6, so it is a solution.

x ≤ 2 or x ≥ 6:
6 does not satisfy this inequality, so it is not a solution.

x < 2 or x > 6:
6 does not satisfy this inequality, so it is not a solution.

x < -5 or x > 0:
6 does not satisfy this inequality, so it is not a solution.

Therefore, the only true statement is -2 ≤ x ≤ 6.

Answer 8

A student scored 85 in her Algebra class before she took the End of Course Exam (the EOC). The student wants her average to be between 80 and 90 inclusive after her EOC is entered into her grades. The EOC counts 1/5 of her overall grade and her class average counts 4/5 of her grade. Write and solve a compound inequality to find the possible score she will need to make on the EOC to get the average she wants for her final grade in the course.(1 point) Responses 80 ≤85 + 85 +85 +85 + x5 ≤ 9080 ≤85 + 85 +85 +85 + x5 ≤ 90; 85 ≤ x ≤ 11085 ≤ x ≤ 11080 ≤85 + 85 +85 +85 + x5 ≤ 9080 ≤85 + 85 +85 +85 + x5 ≤ 90; 85 ≤ x ≤ 11085 ≤ x ≤ 110 80 <85 + 85 +85 +85 + x5 < 9080 <85 + 85 +85 +85 + x5 < 90; 85 < x < 11085 < x < 110 80 <85 + 85 +85 +85 + x5 < 9080 <85 + 85 +85 +85 + x5 < 90; 85 < x < 11085 < x < 110 90 ≤85 + 85 +85 +85 + x5 ≤ 8090 ≤85 + 85 +85 +85 + x5 ≤ 80; 110 ≤ x ≤ 80110 ≤ x ≤ 80 90 ≤85 + 85 +85 +85 + x5 ≤ 8090 ≤85 + 85 +85 +85 + x5 ≤ 80; 110 ≤ x ≤ 80110 ≤ x ≤ 80 90 <85 + 85 +85 +85 + x5 < 8090 <85 + 85 +85 +85 + x5 < 80; 110 < x < 85

Answer 9

[AI-generated answer — Bot GPT 3.5]

Let x be the score she needs to make on the EOC.

Her overall grade will be determined by the formula:
(4/5)(class average) + (1/5)(EOC score)
Since she wants her average to be between 80 and 90 inclusive, we can write the compound inequality:

80 ≤ (4/5)*85 + (1/5)*x ≤ 90

Simplifying the inequality:

80 ≤ (340/5) + (1/5)*x ≤ 90
80 ≤ 68 + (1/5)*x ≤ 90
80 - 68 ≤ (1/5)*x ≤ 90 - 68
12 ≤ (1/5)*x ≤ 22

To isolate x, we multiply all parts of the inequality by 5:

5*12 ≤ 5*((1/5)*x) ≤ 5*22
60 ≤ x ≤ 110

Therefore, she will need to score between 60 and 110 on the EOC to get the average she wants for her final grade.

Answer 10

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.

Answer 11

[AI-generated answer — Bot GPT 3.5]

To represent the amount of revenue Tonisha would need to generate, the inequality would be:

x ≥ 55 + 36

This inequality represents the condition that the revenue x should be greater than or equal to the sum of her expenses ($36) plus the minimum amount she wants to make per day ($55).

Answer 12

Tonisha needs to sell (refer back to the previous answer you selected and solve the inequality)

Answer 13

[AI-generated answer — Bot GPT 3.5]

To solve the inequality x ≥ 55 + 36, we can simplify it to find the minimum revenue required for Tonisha to meet her goal.

x ≥ 91

This means that Tonisha needs to sell lemonade and generate a revenue of at least $91 in order to meet her goal of making $55 per day after accounting for her $36 in expenses.

Answer 14

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

Answer 15

[AI-generated answer — Bot GPT 3.5]

To find the number of trading cards Lamont needs, we can write the inequality:

x + 20 ≤ 50

To solve this inequality, we need to isolate the variable x.

Subtract 20 from both sides:

x ≤ 50 - 20
x ≤ 30

Therefore, the number of trading cards Lamont needs is x ≤ 30.

The true statements are:
- x + 20 ≤ 50
- x ≤ 30

Answer 16

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

Answer 17

[AI-generated answer — Bot GPT 3.5]

To represent the number of hours where Option A will be the cheaper rental company, we can compare the total cost of renting a kayak from each company.

For Company A: Total cost = $10 + $8x, where x represents the number of hours.
For Company B: Total cost = $6 + $10x, where x represents the number of hours.

To find the number of hours (x) where Option A will be cheaper, we can write the inequality:

10 + 8x < 6 + 10x

To solve this inequality, we can isolate the variable x:

8x - 10x < 6 - 10
-2x < -4
x > 2

Therefore, the number of hours (x) where Option A will be the cheaper rental company is x > 2.

Answer 18

Solve and graph the solution to the compound inequality. −4x ≥ 36 or x − 7 ≥ −3

Answer 19

[AI-generated answer — Bot GPT 3.5]

To solve the compound inequality, we need to solve each inequality separately and then combine the solutions.

First, let's solve the inequality -4x ≥ 36:

Divide both sides by -4, remembering to flip the direction of the inequality when dividing by a negative number:

x ≤ -36/4
x ≤ -9

Next, let's solve the inequality x - 7 ≥ -3:

Add 7 to both sides of the inequality:

x ≥ -3 + 7
x ≥ 4

Now, let's combine the solutions:

The solution to the compound inequality is x ≤ -9 or x ≥ 4.

To graph the solution, we can represent it on a number line:
```
-inf -9 ----------------------------- 4 +inf
[ o-------------|---------------------o ]
x ≤ -9 x ≥ 4
```

The shaded region represents the values of x that satisfy the compound inequality.

Answer 20

Solve and graph the compound inequality on a number line. x4 < −1 and x + 6 > −2

Answer 21

[AI-generated answer — Bot GPT 3.5]

To solve the compound inequality, we will solve each inequality separately and then combine the solutions.

1. x + 4 < -1:
Subtract 4 from both sides of the inequality:
x < -5

2. x + 6 > -2:
Subtract 6 from both sides of the inequality:
x > -8

The solution to the compound inequality is x < -5 and x > -8, meaning x is any value less than -5 or greater than -8.

To graph the solution on a number line:
```
-inf -8 -5 +inf
[-----o----o----->
x < -5
-8 < x
```

The open circles represent the points that are not included in the solution set (-5 and -8), and the arrowheads indicate that the solution extends indefinitely in each direction.

Answer 22

Write an Inequality that represents the graph below. (1 point) Responses b > -4 and b ≤ -7 b > -4 and b ≤ -7 b > -4 or b < -7 b > -4 or b < -7 b > -4 or b ≤ -7 b > -4 or b ≤ -7 b > -4 and b < -7

Answer 23

[AI-generated answer — Bot GPT 3.5]

To represent the graph below, we can write the inequality:

b > -4 and b ≤ -7

This inequality states that b is greater than -4 and less than or equal to -7.