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

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

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

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

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

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

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

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

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

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

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