Compound Inequalities Word problems

**Page 1**

1.

Which of the following choices describes the solution of the inequality 2 < $x$ + 5 < 6?

a. | $x$ is greater than -3 and less than 1 | ||

b. | $x$ is greater than 3 and less than 1 | ||

c. | $x$ is greater than -3 and less than - 1 | ||

d. | $x$ is greater than 3 and less than -1 |

[Original inequality.]

2 - 5 <

[Subtract 5 from each expression.]

-3 <

[Simplify.]

The compound inequality may be described as '

Correct answer : (1)

2.

Which of the following best describes the solution of the inequality -3 < $x$ + 4 ≤ 5?

a. | $x$ greater than or equal to -7 and less than 1 | ||

b. | $x$ greater than -7 and less than or equal to 1 | ||

c. | $x$ greater than -7 and greater than or equal to 1 | ||

d. | $x$ less than -7 and less than or equal to 1 |

[Original inequality.]

-3 - 4 <

[Subtract 4 from each expression.]

-7 <

[Simplify.]

The compound inequality may be described as '

Correct answer : (2)

3.

Which of the following choices describes the solution of the inequality 0 < $x$ + 7 < 9?

a. | $x$ is greater than -7 and less than 2 | ||

b. | $x$ is greater than -7 and less than - 2 | ||

c. | $x$ is greater than 7 and less than 2 | ||

d. | $x$ is greater than 7 and less than - 2 |

[Original inequality.]

0 - 7 <

[Subtract 7 from each expression.]

-7 <

[Simplify.]

The compound inequality may be described as '

Correct answer : (1)

4.

The audible frequency range of a dog is 25 Hz to 50000 Hz. Write an inequality to describe the frequency range of $f$.

a. | 25 ≤ $f$ ≤ 50000 | ||

b. | 25 < $f$ < 50000 | ||

c. | 25 < $f$ ≤ 50000 | ||

d. | 25 ≤ $f$ < 50000 |

[Express in the form of inequalities.]

25 ≤

[Combine into a single inequality.]

So, the compound inequality 25 ≤

Correct answer : (1)

5.

Which of the following compound inequalities represents the set of real numbers greater than or equal to - 3 and less than 3?

a. | -3 ≤ $x$ ≤ 3 | ||

b. | -3 ≤ $x$ < 3 | ||

c. | -3 < $x$ ≤ 3 | ||

d. | -3 < $x$ < 3 |

[Expressing the statement as two inequalities.]

-3 ≤

[Combine into single inequality.]

Correct answer : (2)

6.

Which of the following compound inequalities represents the set of real numbers less than 6 and greater than 1?

a. | 1 ≤ $x$ < 6 | ||

b. | 1 < $x$ ≤ 6 | ||

c. | 1 ≤ $x$ ≤ 6 | ||

d. | 1 < $x$ < 6 |

[Express the statement as two inequalities.]

1 <

[Combine into single inequality.]

Correct answer : (4)

7.

The oxygen percent decreases as the elevation increases. If $h$ represents the elevation, find the oxygen percentage that shows the compound inequality 25000 < $h$ ≤ 50000 from the table.

a. | 14% | ||

b. | 6% | ||

c. | 50% | ||

d. | 35% |

The percentage of oxygen for the above range of elevation from the table is 6%.

Correct answer : (2)

8.

If $y$ represents the elevation in feet, write a compound inequality that describes the approximate elevation range for 35% of oxygen.

a. | 10000 > $y$ ≥ 25000 | ||

b. | 10000 < $y$ ≤ 25000 | ||

c. | 10000 ≤ $y$ ≤ 25000 | ||

d. | 10000 < $y$ ≥ 25000 |

1000 ≤

[Combine into single inequalit

Correct answer : (2)

9.

Which of the follwoing choices describes the solution of the inequality 1 ≤ 3$x$ - 2 ≤ 4?

a. | $x$ is greater than or equal to 1 and less than or equal to 2 | ||

b. | $x$ is greater than or equal to 1 and less than or equal to 3 | ||

c. | $x$ is greater than or equal to1 and less than or equal to 4 | ||

d. | None of the above |

[Original inequality.]

1 + 2 ≤ 3

[Add 2 to each expression.]

3 ≤ 3

[Simplify.]

[Divide each expression by 3.]

1 ≤

[Simplify.]

The compound inequality in verbal sentence is '

Correct answer : (1)

10.

Write a verbal sentence that describes the simplified inequality -3 ≤ -$x$ + 3 < 5.

a. | $x$ is greater than or equal to 2 and less than -6 | ||

b. | $x$ is greater than -2 and less than or equal to 6 | ||

c. | $x$ is greater than or equal to -2 and less than or equal to 6 | ||

d. | None of the above |

[Original inequality.]

-3 - 3 ≤ -

[Subtract 3 from each e

-6 ≤ -

[Simplify.]

-1(-6) ≥ -1(-

[Multiply each e

6 ≥

[Simplify.]

The compound inequality in verbal sentence is '

Correct answer : (2)