Question
15.) You need to buy some pencils and an eraser. You must spend less than $5. The eraser costs $1 and the pencils cost .27 cents each. Write an inequality to represent the situation then find the maximum number of pencils you can buy.
*
.27p + 1 < 5 ; The maximum number of pencils that can be purchased is 15.
.27p + 1 < 5 ; The maximum number of pencils that can be purchased is 14.
5p - 27 < 1 ; The maximum number of pencils that can be purchased is 5.
5p - 27 < 1 ; The maximum number of pencils that can be purchased is 6.
9.) Solve the inequality.
5.72x + 1.32 > 9.9
*
x > 1.96
x > 1.5
x > 2.25
x > 5.6
2.) Solve the inequality.
*
Captionless Image
Option 1
Option 2
Option 3
Option 4
3.) Jill solved an inequality and graphed the solution on the number line. Which of the following inequalities did she solve?
*
Captionless Image
Option 1
Option 2
Option 4
Option 3
8.) Solve the inequality.
*
Captionless Image
Option 1
Option 2
Option 3
Option 4
12.) Bill is taking a trip on an airplane. He knows that to avoid extra fees his suitcase must weigh under 45 pounds. The suitcase with his clothes weighs 40 pounds. He has room so he decides to pack some books for his trip, too. Each book weighs 1.5 pounds. He writes the inequality 1.5b + 40 < 45, where b equals the number of books, to help figure this out. Solve his inequality to determine how many whole books he can bring on his trip.
*
He can bring 4 books.
He can bring 5 books.
He can bring 2 books.
He can bring 3 books.
7.) Peggy solve an inequality and graphed the solution on the number line. Which of the following inequalities did she solve?
*
Captionless Image
3.7x < 7.4
4.9x < 9.31
2.1x > 4.2
12.6x > 26.46
16.) Seven more than 3 times a number is less than 10. Write an inequality to represent the situtation.
*
7x + 3 < 10
3x + 7 < 10
3x - 10 > 7
7x - 10 < 3
6.) Solve the inequality.
5.4x < 32.4
*
x < 27
x > 1.6
x > 37.8
x < 6
11.) Ten more than three times a number is less than 50. Write an inequality that could be used to solve this problem.
*
3x + 50 < 10
3x + 10 < 50
50 - x < 10
10x - 3 < 50
13.) Mary has a goal of taking 8,000 more steps today. According to her pedometer, she has gotten 2,500 steps in so far today. There are 5 hours left in the day. How many steps will she need to get each hour (assume she walks the same number of steps each hour) for the rest of the day to meet her goal? Write an inequality to model this situation then solve.
*
5x + 2500 > 8000; x > 2,100
2500x - 5x < 8000; x < 3,200
5x + 2500 > 8000 ; x > 1,100
5x + 8000 < 2500; x < 2,100
10.) Which of the following inequalities shows the solution on the number line?
*
Captionless Image
4.3x + 3.2 > 13.95
2.5x + 9.1 < 15.35
5.3x - 7.2 > 3.4
2.5x + 3 > 5
1.) Solve the inequality.
*
Captionless Image
Option 4
Option 1
Option 3
Option 2
4.) Solve the inequality.
*
Captionless Image
Option 1
Option 3
Option 4
Option 2
5.) Solve the inequality.
7x > 35
*
x < 5
x > -5
x > 28
x > 5
14.) What inequality is shown on the graph?
*
Captionless Image
m < -6
m > -6
m < 5
m > 5
17.) What is the solution to the inequality:
2y + 7 < 21
*
y < 28
y < 3
y < 14
y < 7
*
.27p + 1 < 5 ; The maximum number of pencils that can be purchased is 15.
.27p + 1 < 5 ; The maximum number of pencils that can be purchased is 14.
5p - 27 < 1 ; The maximum number of pencils that can be purchased is 5.
5p - 27 < 1 ; The maximum number of pencils that can be purchased is 6.
9.) Solve the inequality.
5.72x + 1.32 > 9.9
*
x > 1.96
x > 1.5
x > 2.25
x > 5.6
2.) Solve the inequality.
*
Captionless Image
Option 1
Option 2
Option 3
Option 4
3.) Jill solved an inequality and graphed the solution on the number line. Which of the following inequalities did she solve?
*
Captionless Image
Option 1
Option 2
Option 4
Option 3
8.) Solve the inequality.
*
Captionless Image
Option 1
Option 2
Option 3
Option 4
12.) Bill is taking a trip on an airplane. He knows that to avoid extra fees his suitcase must weigh under 45 pounds. The suitcase with his clothes weighs 40 pounds. He has room so he decides to pack some books for his trip, too. Each book weighs 1.5 pounds. He writes the inequality 1.5b + 40 < 45, where b equals the number of books, to help figure this out. Solve his inequality to determine how many whole books he can bring on his trip.
*
He can bring 4 books.
He can bring 5 books.
He can bring 2 books.
He can bring 3 books.
7.) Peggy solve an inequality and graphed the solution on the number line. Which of the following inequalities did she solve?
*
Captionless Image
3.7x < 7.4
4.9x < 9.31
2.1x > 4.2
12.6x > 26.46
16.) Seven more than 3 times a number is less than 10. Write an inequality to represent the situtation.
*
7x + 3 < 10
3x + 7 < 10
3x - 10 > 7
7x - 10 < 3
6.) Solve the inequality.
5.4x < 32.4
*
x < 27
x > 1.6
x > 37.8
x < 6
11.) Ten more than three times a number is less than 50. Write an inequality that could be used to solve this problem.
*
3x + 50 < 10
3x + 10 < 50
50 - x < 10
10x - 3 < 50
13.) Mary has a goal of taking 8,000 more steps today. According to her pedometer, she has gotten 2,500 steps in so far today. There are 5 hours left in the day. How many steps will she need to get each hour (assume she walks the same number of steps each hour) for the rest of the day to meet her goal? Write an inequality to model this situation then solve.
*
5x + 2500 > 8000; x > 2,100
2500x - 5x < 8000; x < 3,200
5x + 2500 > 8000 ; x > 1,100
5x + 8000 < 2500; x < 2,100
10.) Which of the following inequalities shows the solution on the number line?
*
Captionless Image
4.3x + 3.2 > 13.95
2.5x + 9.1 < 15.35
5.3x - 7.2 > 3.4
2.5x + 3 > 5
1.) Solve the inequality.
*
Captionless Image
Option 4
Option 1
Option 3
Option 2
4.) Solve the inequality.
*
Captionless Image
Option 1
Option 3
Option 4
Option 2
5.) Solve the inequality.
7x > 35
*
x < 5
x > -5
x > 28
x > 5
14.) What inequality is shown on the graph?
*
Captionless Image
m < -6
m > -6
m < 5
m > 5
17.) What is the solution to the inequality:
2y + 7 < 21
*
y < 28
y < 3
y < 14
y < 7
Answers
GPT-4o mini
Here are the solutions and explanations for each of the problems you provided:
### 15.) Buying Pencils and an Eraser
The inequality representing the situation is:
\[
0.27p + 1 < 5
\]
To find the maximum number of pencils (p), solve the inequality:
\[
0.27p < 4 \quad \text{(subtracting 1 from both sides)}
\]
\[
p < \frac{4}{0.27} \approx 14.81
\]
Since we cannot buy a fraction of a pencil, the maximum number of whole pencils you can buy is **14**.
### 9.) Solve the inequality
The inequality to solve is:
\[
5.72x + 1.32 > 9.9
\]
Subtract 1.32 from both sides:
\[
5.72x > 8.58
\]
Now divide by 5.72:
\[
x > \frac{8.58}{5.72} \approx 1.5
\]
**Correct answer: \( x > 1.5 \)**
### 12.) Bill's Suitcase
The inequality is:
\[
1.5b + 40 < 45
\]
Subtract 40 from both sides:
\[
1.5b < 5
\]
Now divide by 1.5:
\[
b < \frac{5}{1.5} \approx 3.33
\]
So he can bring **3 books**.
### 16.) Seven More than 3 Times a Number
The correct inequality is:
\[
3x + 7 < 10
\]
### 6.) Solve the inequality
The inequality is:
\[
5.4x < 32.4
\]
Dividing both sides by 5.4 gives:
\[
x < \frac{32.4}{5.4} \approx 6
\]
**Correct answer: \( x < 6 \)**
### 11.) Ten More than Three Times a Number
The correct inequality is:
\[
3x + 10 < 50
\]
### 13.) Steps Needed
The inequality to model this situation is:
\[
5x + 2500 > 8000
\]
Subtract 2500:
\[
5x > 5500
\]
Divide by 5:
\[
x > 1100
\]
**Correct answer: \( x > 1100 \)**
### 5.) Solve the inequality
The inequality is:
\[
7x > 35
\]
Dividing both sides by 7 gives:
\[
x > 5
\]
**Correct answer: \( x > 5 \)**
### 17.) Solve the inequality
The inequality is:
\[
2y + 7 < 21
\]
Subtracting 7 from both sides gives:
\[
2y < 14
\]
Dividing by 2 gives:
\[
y < 7
\]
**Correct answer: \( y < 7 \)**
For problems that have images or graphs (such as numbers 2, 3, 4, 8, 10, and 14), I cannot see or interpret these without visual references. For those, you'll need to describe the options or graphs for assistance.
### 15.) Buying Pencils and an Eraser
The inequality representing the situation is:
\[
0.27p + 1 < 5
\]
To find the maximum number of pencils (p), solve the inequality:
\[
0.27p < 4 \quad \text{(subtracting 1 from both sides)}
\]
\[
p < \frac{4}{0.27} \approx 14.81
\]
Since we cannot buy a fraction of a pencil, the maximum number of whole pencils you can buy is **14**.
### 9.) Solve the inequality
The inequality to solve is:
\[
5.72x + 1.32 > 9.9
\]
Subtract 1.32 from both sides:
\[
5.72x > 8.58
\]
Now divide by 5.72:
\[
x > \frac{8.58}{5.72} \approx 1.5
\]
**Correct answer: \( x > 1.5 \)**
### 12.) Bill's Suitcase
The inequality is:
\[
1.5b + 40 < 45
\]
Subtract 40 from both sides:
\[
1.5b < 5
\]
Now divide by 1.5:
\[
b < \frac{5}{1.5} \approx 3.33
\]
So he can bring **3 books**.
### 16.) Seven More than 3 Times a Number
The correct inequality is:
\[
3x + 7 < 10
\]
### 6.) Solve the inequality
The inequality is:
\[
5.4x < 32.4
\]
Dividing both sides by 5.4 gives:
\[
x < \frac{32.4}{5.4} \approx 6
\]
**Correct answer: \( x < 6 \)**
### 11.) Ten More than Three Times a Number
The correct inequality is:
\[
3x + 10 < 50
\]
### 13.) Steps Needed
The inequality to model this situation is:
\[
5x + 2500 > 8000
\]
Subtract 2500:
\[
5x > 5500
\]
Divide by 5:
\[
x > 1100
\]
**Correct answer: \( x > 1100 \)**
### 5.) Solve the inequality
The inequality is:
\[
7x > 35
\]
Dividing both sides by 7 gives:
\[
x > 5
\]
**Correct answer: \( x > 5 \)**
### 17.) Solve the inequality
The inequality is:
\[
2y + 7 < 21
\]
Subtracting 7 from both sides gives:
\[
2y < 14
\]
Dividing by 2 gives:
\[
y < 7
\]
**Correct answer: \( y < 7 \)**
For problems that have images or graphs (such as numbers 2, 3, 4, 8, 10, and 14), I cannot see or interpret these without visual references. For those, you'll need to describe the options or graphs for assistance.