- Writing, Graphing and Solving Inequalities
- Home
- Translating a Sentence by Using an Inequality Symbol
- Translating a Sentence into a One-Step Inequality
- Introduction to Identifying Solutions to an Inequality
- Writing an Inequality for a Real-World Situation
- Graphing a Linear Inequality on the Number Line
- Writing an Inequality Given a Graph on the Number Line
- Identifying Solutions to a One-Step Linear Inequality
- Additive Property of Inequality with Whole Numbers
- Multiplicative Property of Inequality with Whole Numbers
- Solving a Two-Step Linear Inequality with Whole Numbers
- Solving a Word Problem Using a One-Step Linear Inequality

- Selected Reading
- UPSC IAS Exams Notes
- Developer's Best Practices
- Questions and Answers
- Effective Resume Writing
- HR Interview Questions
- Computer Glossary
- Who is Who

# Solving a Word Problem Using a One-Step Linear Inequality Online Quiz

Following quiz provides Multiple Choice Questions (MCQs) related to **Solving a Word Problem Using a One-Step Linear Inequality**. You will have to read all the given answers and click over the correct answer. If you are not sure about the answer then you can check the answer using **Show Answer** button. You can use **Next Quiz** button to check new set of questions in the quiz.

**Q 1 - Five more than a number is less than 23. Find the number.**

### Answer : B

### Explanation

**Step 1:**

Let the number be x

**Step 2:**

Five more than the number x translates to

x + 5

**Step 3:**

Five more than a number is less than 23 translates to

x + 5 < 23

**Step 4:**

Subtracting 5 from both sides

x + 5 −5 < 23 – 5; x < 18

So the solution of inequality is

x < 18

**Q 2 - Eight more than a number is greater than or equal to 31. Find the number.**

### Answer : C

### Explanation

**Step 1:**

Let the number be x

**Step 2:**

Eight more than the number x translates to

x + 8

**Step 3:**

Eight more than a number is greater than or equal to 31 translates to

x + 8 ≥ 31

**Step 4:**

Subtracting 8 from both sides

x + 8 −8 ≥ 31 – 8; x ≥ 23

So the solution of inequality is

x ≥ 23

**Q 3 - Eleven less than a number is less than or equal to 24. Find the number.**

### Answer : D

### Explanation

**Step 1:**

Let the number be x

**Step 2:**

Eleven less than the number x translates to

x − 11

**Step 3:**

Eleven less than a number is less than or equal to 24 translates to

x − 11 ≤ 24

**Step 4:**

Adding 11 to both sides

x + 11 −11 ≤ 24 + 11; x ≤ 35

So the solution of inequality is

x ≤ 35

**Q 4 - In 5 years, Nicole will be old enough to vote in an election. The minimum age for voting is at least 18 years. What can you say about how old she is now?**

### Answer : A

### Explanation

**Step 1:**

Let the age of Nicole be x

**Step 2:**

In 5 years, Nicole’s age = x + 5 which is at least 18 years

x + 5 ≥ 18

**Step 3:**

Subtracting 5 from both sides

x + 5 −5 ≥ 18 – 5; x ≥ 13

**Step 4:**

So she is at least 13 years or x ≥ 13

**Q 5 - Brad has a $48 online gift voucher. He plans to buy as many books as he can. The cost of each book is $4. How many books can he afford without spending more than his gift voucher amount?**

### Answer : C

### Explanation

**Step 1:**

Let the number of books be x

**Step 2:**

Cost of each book = $4

Cost of x books = 4x which should be less than or equal to $48

4x ≤ 48

**Step 3:**

Dividing both sides by 4

$\frac{4x}{4}$ ≤ $\frac{48}{4}$; x ≤ 12

**Step 4:**

So not more than 12 books can be bought or

x ≤ 12

**Q 6 - Nine more than a number is greater than 47. Find the number.**

### Answer : A

### Explanation

**Step 1:**

Let the number be x

**Step 2:**

Nine more than the number x translates to

x + 9

**Step 3:**

Nine more than a number is greater than 47 translates to

x + 9 > 47

**Step 4:**

Subtracting 9 from both sides

x + 9 −9 > 47 – 9; x > 38

So the solution of inequality is

x > 38

**Q 7 - While training for a marathon, you consume at least 2100 calories a day. For one session of exercise, you consume 500 calories. How many calories do you consume for the rest of the day?**

### Answer : B

### Explanation

**Step 1:**

Let the number of calories consumed during rest of the day be x

**Step 2:**

Total calories consumed during the day is at least 2100 or ≥ 2100

Calories consumed during exercise session = 500

**Step 3:**

Calories consumed during the day

x + 500 ≥ 2100

Subtracting 500 from both sides

x + 500 – 500 ≥ 2100 – 500;

x ≥ 1600

**Step 4:**

So calories consumed during rest of day is at least 1600 or x ≥ 1600

**Q 8 - Sue has $36 left for a cab fare home. The cab fare is $4 per mile. What is the number of miles she will be able to travel in the cab?**

### Answer : D

### Explanation

**Step 1:**

Let the number of miles that Sue travels in the cab be x

**Step 2:**

Total amount Sue has $36 or ≤ 36

Cab fare per mile is $4

**Step 3:**

Amount of fare if she travels x miles = 4x

4x ≤ 36

Dividing both sides by 4

$\frac{4x}{4}$ ≤ $\frac{36}{4}$

x ≤ 9

**Step 4:**

So the number of miles that Sue can travel in the cab is x ≤ 9

**Q 9 - A teacher charges $2 for a pencil to student who forgot to bring one to class. Nelson was charged at least $28, how many times did he forget his pencil?**

### Answer : D

### Explanation

**Step 1:**

Let the number of times Nelson forgets to bring a pencil be x

**Step 2:**

Total amount charged at least $28 or ≥ 28

Fine charged each time is $2

**Step 3:**

Amount of fine charged for x times = 2x

2x ≥ 28

Dividing both sides by 2

$\frac{2x}{2}$ ≥ $\frac{28}{2}$

x ≥ 14

**Step 4:**

So the number of times Nelson forgot the pencil is x ≥ 14

**Q 10 - Sandra won 46 toffees in a competition. She gives three toffees each of her classmates and has at least 7 toffees left at the end. Find the number of students in her class.**

### Answer : B

### Explanation

**Step 1:**

Let the number of students in the class be x

**Step 2:**

Total number of toffees = 46

Number of toffees given to each student 3

Total toffees given to students = 3x

**Step 3:**

Number of toffees remaining at least 7 or ≥ 7

46 −3x ≥ 7

Subtracting 46 from both sides

46 −3x – 46 ≥ 7 – 46

−3x ≥ − 39

Dividing both sides by −3 and flipping signs

$\frac{−3x}{−3}$ ≤ $\frac{−39}{−3}$; x ≤ 13

**Step 4:**

So the number of students in the class is x ≤ 13