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.

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

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