Solving Inequalities (using Multiplication and Division) Worksheet

**Page 1**

1.

Which numbers are the solutions of the inequality, $x$ + 5 < 3?

a. | 2 | ||

b. | - 1 | ||

c. | - 5 |

The number of lawns mowed from Monday to Saturday = the number of days from Monday to Saturday x the number of lawns mowed on each day = 6 × 1 = 6.

The total number of lawns mowed by {Hename[1]} in a week = 6 + 2 = 8.

[Number of lawns mowed on Sunday = 2.]

The total number of lawns mowed in 3 weeks = 3 × the number of lawns mowed in a week.

= 3 × 8

[Substitute the values.]

The total number of lawns mowed by {Hename[1]} in three weeks is 24.

Correct answer : (4)

2.

Which numbers are the solutions of the inequality, $x$ - 7 > 2?

a. | 9 | ||

b. | 5 | ||

c. | 12 | ||

d. | - 5 |

= {val1} +

The expression that describes the number of {Q18215B[1]}s owned by {Hename[1]} is {val1} +

Correct answer : (3)

3.

Which numbers are the solutions of the inequality, $x$ + 5 < 3?

a. | - 5 | ||

b. | - 1 | ||

c. | 2 |

The number of lawns mowed from Monday to Saturday = the number of days from Monday to Saturday x the number of lawns mowed on each day = 6 × 1 = 6.

The total number of lawns mowed by {Hename[1]} in a week = 6 + 2 = 8.

[Number of lawns mowed on Sunday = 2.]

The total number of lawns mowed in 3 weeks = 3 × the number of lawns mowed in a week.

= 3 × 8

[Substitute the values.]

The total number of lawns mowed by {Hename[1]} in three weeks is 24.

Correct answer : (1)

4.

Which of the choices represents the solution for the inequality, 9$x$ > 81?

a. | $x$ > 9 | ||

b. | $x$ ≤ 9 | ||

c. | $x$ < 9 | ||

d. | $x$ ≥ 9 |

[Original inequality.]

[Divide by 9 on both sides, according to division property, if

[Simplify.]

Correct answer : (1)

5.

Which of the choices represents the solution for the inequality, 3$x$ > 9?

a. | $x$ ≤ 3 | ||

b. | $x$ > 3 | ||

c. | $x$ ≥ 3 | ||

d. | $x$ < 3 |

[Original inequality.]

[Divide by 3 on both sides, according to division property, if

[Simplify.]

Correct answer : (2)

6.

The cost of one xerox copy is 5 cents per page. Francis cannot spend more than 150 cents on xerox. Express the number of pages he can get xeroxed as an inequality.

a. | $x$ > 30 | ||

b. | $x$ < 30 | ||

c. | $x$ ≤ 30 | ||

d. | $x$ ≥ 30 |

5

[Original inequality.]

[Divide each side by 5.]

[Simplify.]

Correct answer : (3)

7.

Solve the inequality - 10$a$ ≤ 50.

a. | $a$ > 5 | ||

b. | $a$ < 5 | ||

c. | $a$ ≥ - 5 | ||

d. | $a$ ≤ - 5 |

[Original equation.]

[Divide each side by - 10 and reverse the direction of the inequality.]

[Simplify.]

Correct answer : (3)

8.

Solve the inequality -6$b$ > 48.

a. | $b$ < -8 | ||

b. | $b$ < 8 | ||

c. | $b$ > -8 | ||

d. | $b$ > 8 |

[Original inequality.]

[Divide each side by -6 and reverse the inequality symbol.]

[Simplify.]

Correct answer : (1)

9.

Solve the inequality - 7$k$ ≥ 56.

a. | $k$ ≥ - 8 | ||

b. | $k$ ≤ - 8 | ||

c. | $k$ ≥ 8 | ||

d. | $k$ ≤ 8 |

[Original inequality.]

[Divide each side by - 7 and reverse the inequality symbol.]

[Simplify.]

Correct answer : (2)

10.

Rebecca has $150, with which she can buy at most 3 dresses. Find the maximum cost of each dress she can buy.

a. | $49 | ||

b. | $51 | ||

c. | $50 | ||

d. | None of the above |

As she can buy at most 3 dresses, the total cost of the 3 dresses is less than or equal to $150.

3

[Write the inequality.]

[Divide by 3 on each side.]

[Simplify.]

The maximum cost of each dress is $50.

[As

Correct answer : (3)