Inequality Word Problems

**Page 1**

1.

The height of a person should not be less than 6 ft to get a police job. Choose an inequality for this situation.

a. | $x$ ≤ 6 | ||

b. | $x$ < 6 | ||

c. | $x$ > 6 | ||

d. | $x$ ≥ 6 |

Let the height of a person be

The inequality that represents the situation is

[Height of a person should be greater than or equal to 6 ft.]

Correct answer : (4)

2.

The price of a ball should not be more than $2. Choose an inequality for this situation.

a. | $x$ ≤ 2 | ||

b. | $x$ < 2 | ||

c. | $x$ ≥ 2 | ||

d. | $x$ > 2 |

Let the price of a ball be

The inequality that represents the situation is

[Price of a ball should be less than or equal to $2.]

Correct answer : (1)

3.

Ashley scores more than 400 marks on an average in all subjects. Choose an inequality to represent this situation.

a. | $x$ < 400 | ||

b. | $x$ ≥ 400 | ||

c. | $x$ ≤ 400 | ||

d. | $x$ > 400 |

Let the average score be

The inequality that represents the situation is

[Average score in all subjects should be greater than 400.]

Correct answer : (4)

4.

The sum of a number and 21 is less than or equal to 37. Find the number.

a. | 14 | ||

b. | 19 | ||

c. | 18 | ||

d. | 17 |

[Write the inequality.]

[Subtract 21 from both sides.]

So, for the values of

Correct answer : (1)

5.

The sum of a number and 12 is greater than or equal to 57. Find the number.

a. | 47 | ||

b. | 43 | ||

c. | 32 | ||

d. | 20 |

[Write the inequality.]

[Subtract 12 from both sides.]

So, for the values of

Correct answer : (1)

6.

Which of the graphs best suits for the inequality $x$ ≥ - 2?

a. | Graph 2 | ||

b. | Graph 1 | ||

c. | Graph 3 | ||

d. | Graph 4 |

All the numbers to the right of the number on the line are greater than the number.

[Values increase from left to right on a number line.]

The graph with the open dot on a number shows that the number is not a solution of the inequality and the graph with the closed dot on a number shows that the number is a solution of the inequality.

The following graph represents the solutions of the inequality.

Correct answer : (4)

7.

Gary has broken the university record of 17.05 seconds for a race. Which of the following cannot be Gary's timing in the race?

a. | 11.85 | ||

b. | 17.05 | ||

c. | 16.05 | ||

d. | 15.75 |

[university record is 17.05 seconds.]

The inequality,

[Let

All the choices except 17.05 are less than 17.05.

[17.05 is equal to 17.05.]

So, Gary's timing cannot be 17.05 seconds, if he breaks the university record.

Correct answer : (2)

8.

Which of the following inequalities best suits the graph?

a. | $x$ < - 4.5 | ||

b. | $x$ ≤ - 5 | ||

c. | $x$ ≥ - 4.5 | ||

d. | $x$ > - 5 |

[Values increase from left to right on a number line.]

An inequality is a statement that compares two expressions, of which one can be a variable.

The graph with the open dot on a number shows that the number is not a solution of the inequality and the graph with the closed dot on a number shows that the number is a solution of the inequality.

The graph has a closed dot on -5. So, -5 is not a solution of the inequality.

Among the choices

Correct answer : (4)

9.

Mrs. Katie has two sons admitted in different schools for kindergarten. The fee for the younger son is $32 and the fee for the elder son is more than the fee for the younger son. Which of the following is not a solution for the inequality expression $f$ that represents the total fee to be paid by Mrs. Katie?

a. | 114 | ||

b. | 74 | ||

c. | 94 | ||

d. | 64 |

The inequality for the total fee

All the values that make the inequality true are the solutions of the inequality.

Among the choices all the values except 64 are greater than 64.

So, 64 is not a solution of the inequality.

Correct answer : (4)

10.

"The University $U$ offers hostel facilities for at most 800 students." Which of the following inequalities represent the situation, if $S$ is the number of students that the hostel can accommodate?

a. | $S$ ≥ 800 | ||

b. | $S$ > 800 | ||

c. | $S$ < 800 | ||

d. | $S$ ≤ 800 |

The inequality for the situation is

Correct answer : (4)