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

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

### 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.

### 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.

### 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:

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?

### 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?

### 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.

### 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?

### 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?

### 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?

### 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.

### 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

solving_a_word_problem_using_one_step_linear_inequality.htm