Question
Paolo solved an inequality and graphed the solution on the number line. Which of the following inequalities did he solve?
Responses
2.8x < 10.5
4.9x > 19.6
3.7x > 14.8
2.1x < 8.4
Explain
Responses
2.8x < 10.5
4.9x > 19.6
3.7x > 14.8
2.1x < 8.4
Explain
Answers
Answer
he did an open circle on 4 going down
Answer
Solve 8x − 14 ≤ 10 . Make sure to write your inequality so that x comes first.
Explain
Explain
Answer
Solve 5.14x + 2.25 > 15.1. Write the rational number in your answer in decimal form to the tenths place. Make sure to write your inequality so that x comes first.
Explain
Explain
Answer
Preston solved an inequality and graphed the solution on the number line. Which of the following inequalities did he solve? He graphed a full circle upwards on 1.5
Responses
2.1x+5.6≥8.75
5.6x−18.9≤0.7
0.9x+2.8≤5.95 0.9
5.95 3.4x−1.2≥4.75
Responses
2.1x+5.6≥8.75
5.6x−18.9≤0.7
0.9x+2.8≤5.95 0.9
5.95 3.4x−1.2≥4.75
Answer
Fifteen less than four times a number is more than 49. What are all the possible values of the number? Write an inequality that could be used to solve this problem. Use the letter x as your variable and write your x term first.
Explain
Explain
Answered by
GPT 3.5
To determine which of the inequalities Paolo solved, we need to look at the given answer choices. Paolo solved an inequality and graphed the solution on the number line.
Looking at the inequalities, we can see that a solution on the number line can be graphed for each of the options. However, we need to find the specific inequality that Paolo solved.
Let's analyze the inequalities one by one:
1) 2.8x < 10.5: This inequality can be solved by dividing both sides by 2.8. The solution would be x < 3.75. On the number line, this would be graphed as an open circle at 3.75 and shading to the left.
2) 4.9x > 19.6: This inequality can be solved by dividing both sides by 4.9. The solution would be x > 4. On the number line, this would be graphed as an open circle at 4 and shading to the right.
3) 3.7x > 14.8: This inequality can be solved by dividing both sides by 3.7. The solution would be x > 4. On the number line, this would be graphed as an open circle at 4 and shading to the right.
4) 2.1x < 8.4: This inequality can be solved by dividing both sides by 2.1. The solution would be x < 4. On the number line, this would be graphed as an open circle at 4 and shading to the left.
From the above analysis, we can see that options 2 and 3 have the same solution and graph on the number line. Therefore, it is likely that Paolo solved either the inequality 4.9x > 19.6 or 3.7x > 14.8. However, without any additional information, it is not possible to determine which specific inequality Paolo solved.
Looking at the inequalities, we can see that a solution on the number line can be graphed for each of the options. However, we need to find the specific inequality that Paolo solved.
Let's analyze the inequalities one by one:
1) 2.8x < 10.5: This inequality can be solved by dividing both sides by 2.8. The solution would be x < 3.75. On the number line, this would be graphed as an open circle at 3.75 and shading to the left.
2) 4.9x > 19.6: This inequality can be solved by dividing both sides by 4.9. The solution would be x > 4. On the number line, this would be graphed as an open circle at 4 and shading to the right.
3) 3.7x > 14.8: This inequality can be solved by dividing both sides by 3.7. The solution would be x > 4. On the number line, this would be graphed as an open circle at 4 and shading to the right.
4) 2.1x < 8.4: This inequality can be solved by dividing both sides by 2.1. The solution would be x < 4. On the number line, this would be graphed as an open circle at 4 and shading to the left.
From the above analysis, we can see that options 2 and 3 have the same solution and graph on the number line. Therefore, it is likely that Paolo solved either the inequality 4.9x > 19.6 or 3.7x > 14.8. However, without any additional information, it is not possible to determine which specific inequality Paolo solved.
Answered by
GPT 3.5
Thank you for providing that additional information. From your description, it seems that the correct inequality that Paolo solved and graphed is 2.1x < 8.4.
When we solve this inequality, we divide both sides by 2.1, and the solution is x < 4. On the number line, this is represented by an open circle at 4 going downwards, indicating that the values of x are less than 4.
Therefore, Paolo solved and graphed the inequality 2.1x < 8.4.
When we solve this inequality, we divide both sides by 2.1, and the solution is x < 4. On the number line, this is represented by an open circle at 4 going downwards, indicating that the values of x are less than 4.
Therefore, Paolo solved and graphed the inequality 2.1x < 8.4.
Answered by
GPT 3.5
To solve the inequality 8x - 14 ≤ 10, we want to isolate the variable x on one side of the inequality.
First, we can add 14 to both sides of the inequality:
8x - 14 + 14 ≤ 10 + 14
This simplifies to:
8x ≤ 24
Next, we divide both sides of the inequality by 8 to solve for x:
8x/8 ≤ 24/8
This simplifies to:
x ≤ 3
So, the solution to the inequality 8x - 14 ≤ 10 is x ≤ 3.
First, we can add 14 to both sides of the inequality:
8x - 14 + 14 ≤ 10 + 14
This simplifies to:
8x ≤ 24
Next, we divide both sides of the inequality by 8 to solve for x:
8x/8 ≤ 24/8
This simplifies to:
x ≤ 3
So, the solution to the inequality 8x - 14 ≤ 10 is x ≤ 3.
Answered by
GPT 3.5
To solve the inequality 5.14x + 2.25 > 15.1, we want to isolate the variable x on one side of the inequality.
First, we can subtract 2.25 from both sides of the inequality:
5.14x + 2.25 - 2.25 > 15.1 - 2.25
This simplifies to:
5.14x > 12.85
Next, we divide both sides of the inequality by 5.14 to solve for x:
(5.14x)/5.14 > 12.85/5.14
This simplifies to:
x > 2.5
So, the solution to the inequality 5.14x + 2.25 > 15.1 is x > 2.5.
First, we can subtract 2.25 from both sides of the inequality:
5.14x + 2.25 - 2.25 > 15.1 - 2.25
This simplifies to:
5.14x > 12.85
Next, we divide both sides of the inequality by 5.14 to solve for x:
(5.14x)/5.14 > 12.85/5.14
This simplifies to:
x > 2.5
So, the solution to the inequality 5.14x + 2.25 > 15.1 is x > 2.5.
Answered by
GPT 3.5
From the given information, Preston solved an inequality and graphed a full circle upwards on 1.5 on the number line.
Analyzing the answer choices:
1) 2.1x + 5.6 ≥ 8.75: This inequality does not involve the number 1.5, so it is not the one Preston solved.
2) 5.6x - 18.9 ≤ 0.7: This inequality also does not involve 1.5, so it is not the one Preston solved.
3) 0.9x + 2.8 ≤ 5.95: This inequality does not involve 1.5, so it is not the one Preston solved.
4) 3.4x - 1.2 ≥ 4.75: This inequality does involve the number 1.5. To find out if this is the one Preston solved, we need to solve it:
We can start by adding 1.2 to both sides of the inequality:
3.4x - 1.2 + 1.2 ≥ 4.75 + 1.2
This simplifies to:
3.4x ≥ 5.95
Next, we divide both sides of the inequality by 3.4 to solve for x:
(3.4x)/3.4 ≥ 5.95/3.4
This simplifies to:
x ≥ 1.75
The solution to this inequality is x ≥ 1.75. However, this does not match the graphing description provided. Since Preston graphed a full circle upwards on 1.5, it is clear that the correct inequality that he solved and graphed is not among the given answer choices.
Analyzing the answer choices:
1) 2.1x + 5.6 ≥ 8.75: This inequality does not involve the number 1.5, so it is not the one Preston solved.
2) 5.6x - 18.9 ≤ 0.7: This inequality also does not involve 1.5, so it is not the one Preston solved.
3) 0.9x + 2.8 ≤ 5.95: This inequality does not involve 1.5, so it is not the one Preston solved.
4) 3.4x - 1.2 ≥ 4.75: This inequality does involve the number 1.5. To find out if this is the one Preston solved, we need to solve it:
We can start by adding 1.2 to both sides of the inequality:
3.4x - 1.2 + 1.2 ≥ 4.75 + 1.2
This simplifies to:
3.4x ≥ 5.95
Next, we divide both sides of the inequality by 3.4 to solve for x:
(3.4x)/3.4 ≥ 5.95/3.4
This simplifies to:
x ≥ 1.75
The solution to this inequality is x ≥ 1.75. However, this does not match the graphing description provided. Since Preston graphed a full circle upwards on 1.5, it is clear that the correct inequality that he solved and graphed is not among the given answer choices.
Answered by
GPT 3.5
To solve this problem, we can start by translating the given sentence into an equation or inequality.
Let's use the letter "x" as our variable to represent the number.
The phrase "four times a number" can be represented as 4x.
The phrase "fifteen less than four times a number" can be represented as 4x - 15.
The phrase "more than 49" can be represented as > 49.
Putting it all together, we can write the inequality:
4x - 15 > 49
This inequality represents "fifteen less than four times a number is more than 49."
To solve this inequality and find the possible values of the number, we can follow these steps:
1. Add 15 to both sides of the inequality:
4x - 15 + 15 > 49 + 15.
This simplifies to 4x > 64.
2. Divide both sides of the inequality by 4:
(4x)/4 > 64/4.
This simplifies to x > 16.
So, the range of possible values for the number x is x > 16. This means that any value of x greater than 16 satisfies the inequality.
Let's use the letter "x" as our variable to represent the number.
The phrase "four times a number" can be represented as 4x.
The phrase "fifteen less than four times a number" can be represented as 4x - 15.
The phrase "more than 49" can be represented as > 49.
Putting it all together, we can write the inequality:
4x - 15 > 49
This inequality represents "fifteen less than four times a number is more than 49."
To solve this inequality and find the possible values of the number, we can follow these steps:
1. Add 15 to both sides of the inequality:
4x - 15 + 15 > 49 + 15.
This simplifies to 4x > 64.
2. Divide both sides of the inequality by 4:
(4x)/4 > 64/4.
This simplifies to x > 16.
So, the range of possible values for the number x is x > 16. This means that any value of x greater than 16 satisfies the inequality.