Use the image to answer the question.
Josie solved an inequality and graphed the solution on the number line. Which or the following inequalities did she solve?
(1 point)
Responses
x - 1.25 ≥
1.25
x - 1.25 is greater than or equal to 1.25
x + 0.5 < 3
x + 0.5 < 3
x + 1.25 ≥
1.25
x + 1.25 is greater than or equal to 1.25
x - 1.25 ≤
1.25
13 answers
As an AI, I'm unable to view images directly. To assist you with determining which inequality Josie solved, please either provide a description of how the solution is graphed on the number line or upload the image through an interface that supports image uploads. If you describe the graph for me (for example, telling me where the shading starts, whether it’s a solid or open circle, and which direction the shading extends), I can help you identify the correct inequality.
Solve 1.7x ≥ 5.95
(1 point)
Responses
x ≥
10.115
x is greater than or equal to 10.115
x ≥
4.25
x is greater than or equal to 4.25
x ≥
3.5
x is greater than or equal to 3.5
x ≥
7.65
(1 point)
Responses
x ≥
10.115
x is greater than or equal to 10.115
x ≥
4.25
x is greater than or equal to 4.25
x ≥
3.5
x is greater than or equal to 3.5
x ≥
7.65
To solve the inequality 1.7x ≥ 5.95, you need to isolate x. Do this by dividing both sides of the inequality by 1.7:
1.7x / 1.7 ≥ 5.95 / 1.7
x ≥ 3.5
So, the correct response is:
x ≥ 3.5
x is greater than or equal to 3.5
1.7x / 1.7 ≥ 5.95 / 1.7
x ≥ 3.5
So, the correct response is:
x ≥ 3.5
x is greater than or equal to 3.5
Solve 7x + 9 < 58(1 point)
Responses
x < 343
x < 343
x < 397
x < 397
x < 947
x < 9 and 4 sevenths
x < 7
Responses
x < 343
x < 343
x < 397
x < 397
x < 947
x < 9 and 4 sevenths
x < 7
To solve the inequality 7x + 9 < 58, follow these steps:
1. Subtract 9 from both sides of the inequality to isolate the term with x:
7x + 9 - 9 < 58 - 9
2. Simplify both sides:
7x < 49
3. Divide both sides by 7 to solve for x:
7x / 7 < 49 / 7
x < 7
Thus, the correct response is:
x < 7
1. Subtract 9 from both sides of the inequality to isolate the term with x:
7x + 9 - 9 < 58 - 9
2. Simplify both sides:
7x < 49
3. Divide both sides by 7 to solve for x:
7x / 7 < 49 / 7
x < 7
Thus, the correct response is:
x < 7
Eric is solving the inequality 9x + 15 ≥
51 and graphing the solution. Which of the following describe the steps he should take using inverse operations to solve? (1 point)
Responses
Divide both sides of the inequality by 9 and then add 15 to both sides of the inequality.
Divide both sides of the inequality by 9 and then add 15 to both sides of the inequality.
Divide both sides of the inequality by 9 and then subtract 15 from both sides of the inequality.
Divide both sides of the inequality by 9 and then subtract 15 from both sides of the inequality.
Subtract 15 from both sides of the inequality and then divide both sides of the inequality by 9.
Subtract 15 from both sides of the inequality and then divide both sides of the inequality by 9.
Subtract 15 from both sides of the inequality and then multiply both sides of the inequality by 9.
Subtract 15 from both sides of the inequality and then multiply both sides of the inequality by 9.
Question 2
Help Eric draw his answer on the number line by selecting the correct responses below.
(2 points)
Eric would plot the point given in the solution on the number line with a(n)
circle and shade to the
of the point on the number line.
51 and graphing the solution. Which of the following describe the steps he should take using inverse operations to solve? (1 point)
Responses
Divide both sides of the inequality by 9 and then add 15 to both sides of the inequality.
Divide both sides of the inequality by 9 and then add 15 to both sides of the inequality.
Divide both sides of the inequality by 9 and then subtract 15 from both sides of the inequality.
Divide both sides of the inequality by 9 and then subtract 15 from both sides of the inequality.
Subtract 15 from both sides of the inequality and then divide both sides of the inequality by 9.
Subtract 15 from both sides of the inequality and then divide both sides of the inequality by 9.
Subtract 15 from both sides of the inequality and then multiply both sides of the inequality by 9.
Subtract 15 from both sides of the inequality and then multiply both sides of the inequality by 9.
Question 2
Help Eric draw his answer on the number line by selecting the correct responses below.
(2 points)
Eric would plot the point given in the solution on the number line with a(n)
circle and shade to the
of the point on the number line.
To solve the inequality \( 9x + 15 ≥ 51 \) using inverse operations, Eric should:
1. Subtract 15 from both sides of the inequality to isolate the term with \( x \):
\( 9x + 15 - 15 ≥ 51 - 15 \)
2. Simplify both sides:
\( 9x ≥ 36 \)
3. Divide both sides by 9 to solve for \( x \):
\( \frac{9x}{9} ≥ \frac{36}{9} \)
\( x ≥ 4 \)
So, the correct step is:
Subtract 15 from both sides of the inequality and then divide both sides of the inequality by 9.
Now for graphing the solution on a number line:
1. Eric would plot the point 4 on the number line with a solid circle because the inequality includes the equals sign (≥), which means the value 4 is included in the solution.
2. He should shade to the right of the point on the number line because \( x \) is greater than or equal to 4, indicating all values to the right of 4 are part of the solution set (towards increasing numbers).
Hence, the correct response for graphing would be:
Eric would plot the point given in the solution on the number line with a solid circle and shade to the right of the point on the number line.
1. Subtract 15 from both sides of the inequality to isolate the term with \( x \):
\( 9x + 15 - 15 ≥ 51 - 15 \)
2. Simplify both sides:
\( 9x ≥ 36 \)
3. Divide both sides by 9 to solve for \( x \):
\( \frac{9x}{9} ≥ \frac{36}{9} \)
\( x ≥ 4 \)
So, the correct step is:
Subtract 15 from both sides of the inequality and then divide both sides of the inequality by 9.
Now for graphing the solution on a number line:
1. Eric would plot the point 4 on the number line with a solid circle because the inequality includes the equals sign (≥), which means the value 4 is included in the solution.
2. He should shade to the right of the point on the number line because \( x \) is greater than or equal to 4, indicating all values to the right of 4 are part of the solution set (towards increasing numbers).
Hence, the correct response for graphing would be:
Eric would plot the point given in the solution on the number line with a solid circle and shade to the right of the point on the number line.
on the last question is it open or closed
For the inequality \( 9x + 15 \geq 51 \), after solving, we get \( x \geq 4 \). Since the inequality symbol is greater than or equal to (\(\geq\)), this includes the number 4 as part of the solution set.
To represent this on a number line, you would use a closed circle at the number 4, indicating that 4 is included in the set of solutions.
So the correct graphing representation on the number line includes a closed circle at the point corresponding to \( x = 4 \), with shading to the right to represent all the numbers greater than or equal to 4.
To represent this on a number line, you would use a closed circle at the number 4, indicating that 4 is included in the set of solutions.
So the correct graphing representation on the number line includes a closed circle at the point corresponding to \( x = 4 \), with shading to the right to represent all the numbers greater than or equal to 4.
Suzie earns $300 per week plus $15 per sale at her job. She is hoping to make at least $600 this week. How many sales will she need to make? Suzie writes the inequality 15x + 300 ≥
600, where x equals the number of sales, to help figure this out. Solve her inequality. (1 point)
Responses
x ≥
1.95
x is greater than or equal to 1.95
x ≥
60
x is greater than or equal to 60
x ≥
4,500
x is greater than or equal to 4,500
x ≥
20
600, where x equals the number of sales, to help figure this out. Solve her inequality. (1 point)
Responses
x ≥
1.95
x is greater than or equal to 1.95
x ≥
60
x is greater than or equal to 60
x ≥
4,500
x is greater than or equal to 4,500
x ≥
20
To solve the inequality that represents Suzie's earnings, we have:
\( 15x + 300 \geq 600 \)
Here, \( x \) represents the number of sales Suzie needs to make. To find \( x \), follow these steps:
1. Subtract 300 from both sides to isolate the term with \( x \):
\( 15x + 300 - 300 \geq 600 - 300 \)
2. Simplify:
\( 15x \geq 300 \)
3. Divide both sides by 15 to solve for \( x \):
\( \frac{15x}{15} \geq \frac{300}{15} \)
\( x \geq 20 \)
So Suzie will need to make at least 20 sales to earn at least $600 this week.
The correct response is:
x ≥ 20
x is greater than or equal to 20
\( 15x + 300 \geq 600 \)
Here, \( x \) represents the number of sales Suzie needs to make. To find \( x \), follow these steps:
1. Subtract 300 from both sides to isolate the term with \( x \):
\( 15x + 300 - 300 \geq 600 - 300 \)
2. Simplify:
\( 15x \geq 300 \)
3. Divide both sides by 15 to solve for \( x \):
\( \frac{15x}{15} \geq \frac{300}{15} \)
\( x \geq 20 \)
So Suzie will need to make at least 20 sales to earn at least $600 this week.
The correct response is:
x ≥ 20
x is greater than or equal to 20
Ellie is saving to buy a phone. She wants to have at least $299 saved before buying one. She currently has $213 saved, and she receives $10 a week as an allowance from her parents. After how many weeks will Ellie have enough money saved? Write an inequality that could be used to solve this problem. (1 point)
Responses
10w + 213 ≤
299, where w is the number of weeks.
10w + 213 is less than or equal to 299, where w is the number of weeks.
213w + 10 ≤
299, where w is the number of weeks.
213w + 10 is less than or equal to 299, where w is the number of weeks.
10w + 213 ≥
299, where w is the number of weeks.
10w + 213 is greater than or equal to 299, where w is the number of weeks.
213w + 10 ≥
299, where w is the number of weeks.
213w + 10 is greater than or equal to 299, where w is the number of weeks.
Question 2
Solve the inequality and make sure to show each step of using inverse operations. After how many weeks will Ellie have enough money saved?
(3 points possible; 2 points for explaining the inverse operations to solve and 1 point for correct answer)
Responses
10w + 213 ≤
299, where w is the number of weeks.
10w + 213 is less than or equal to 299, where w is the number of weeks.
213w + 10 ≤
299, where w is the number of weeks.
213w + 10 is less than or equal to 299, where w is the number of weeks.
10w + 213 ≥
299, where w is the number of weeks.
10w + 213 is greater than or equal to 299, where w is the number of weeks.
213w + 10 ≥
299, where w is the number of weeks.
213w + 10 is greater than or equal to 299, where w is the number of weeks.
Question 2
Solve the inequality and make sure to show each step of using inverse operations. After how many weeks will Ellie have enough money saved?
(3 points possible; 2 points for explaining the inverse operations to solve and 1 point for correct answer)
To represent Ellie's savings situation with an inequality, we need to express the total amount saved as her current savings plus the amount she saves over time with her allowance. Since she wants to have at least $299 saved, the inequality will reflect the amount being greater than or equal to $299. Here is the appropriate inequality:
\( 10w + 213 \geq 299 \), where \( w \) is the number of weeks.
Now, let's solve the inequality:
1. Subtract 213 from both sides to isolate the term with \( w \):
\( 10w + 213 - 213 \geq 299 - 213 \)
2. Simplify:
\( 10w \geq 86 \)
3. Divide both sides by 10 to solve for \( w \):
\( \frac{10w}{10} \geq \frac{86}{10} \)
\( w \geq 8.6 \)
Since Ellie cannot save for a fraction of a week, she will need to save for at least 9 full weeks to have enough money to buy the phone.
Here is the solution broken down by points:
1. (1 point) The correct inequality to represent Ellie's savings over time is \( 10w + 213 \geq 299 \), where \( w \) is the number of weeks.
2. (2 points) The steps for solving the inequality using inverse operations are:
- Subtract 213 from both sides of the inequality.
- Divide both sides by 10.
3. (1 point) Ellie will have enough money saved after at least 9 weeks.
\( 10w + 213 \geq 299 \), where \( w \) is the number of weeks.
Now, let's solve the inequality:
1. Subtract 213 from both sides to isolate the term with \( w \):
\( 10w + 213 - 213 \geq 299 - 213 \)
2. Simplify:
\( 10w \geq 86 \)
3. Divide both sides by 10 to solve for \( w \):
\( \frac{10w}{10} \geq \frac{86}{10} \)
\( w \geq 8.6 \)
Since Ellie cannot save for a fraction of a week, she will need to save for at least 9 full weeks to have enough money to buy the phone.
Here is the solution broken down by points:
1. (1 point) The correct inequality to represent Ellie's savings over time is \( 10w + 213 \geq 299 \), where \( w \) is the number of weeks.
2. (2 points) The steps for solving the inequality using inverse operations are:
- Subtract 213 from both sides of the inequality.
- Divide both sides by 10.
3. (1 point) Ellie will have enough money saved after at least 9 weeks.