﻿ Solving Inequalities (using Multiplication and Division) Worksheet | Problems & Solutions

# Solving Inequalities (using Multiplication and Division) Worksheet

Solving Inequalities (using Multiplication and Division) Worksheet
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1.
Which numbers are the solutions of the inequality, $x$ + 5 < 3?
 a. 2 b. - 1 c. - 5

#### Solution:

The total number of lawns mowed by {Hename[1]} in a week = the number of lawns mowed from Monday to Saturday + the number of lawns mowed on Sunday.

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.

2.
Which numbers are the solutions of the inequality, $x$ - 7 > 2?
 a. 9 b. 5 c. 12 d. - 5

#### Solution:

Total number of {Q18215B[1]}s owned = {val1} + Number by which they are increased

= {val1} + z

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

3.
Which numbers are the solutions of the inequality, $x$ + 5 < 3?
 a. - 5 b. - 1 c. 2

#### Solution:

The total number of lawns mowed by {Hename[1]} in a week = the number of lawns mowed from Monday to Saturday + the number of lawns mowed on Sunday.

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.

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

#### Solution:

9x > 81
[Original inequality.]

9x9 > 81 / 9
[Divide by 9 on both sides, according to division property, if c > 0 and a > b then ac > bc.]

x > 9
[Simplify.]

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

#### Solution:

3x > 9
[Original inequality.]

3x3 > 9 / 3
[Divide by 3 on both sides, according to division property, if c > 0 and a > b then ac > bc.]

x > 3
[Simplify.]

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

#### Solution:

Let x be the number of pages he can get xeroxed.

5x ≤ 150
[Original inequality.]

5x51505
[Divide each side by 5.]

x ≤ 30
[Simplify.]

7.
Solve the inequality - 10$a$ ≤ 50.
 a. $a$ > 5 b. $a$ < 5 c. $a$ ≥ - 5 d. $a$ ≤ - 5

#### Solution:

- 10a ≤ 50
[Original equation.]

- 10a- 1050- 10
[Divide each side by - 10 and reverse the direction of the inequality.]

a ≥ - 5
[Simplify.]

8.
Solve the inequality -6$b$ > 48.
 a. $b$ < -8 b. $b$ < 8 c. $b$ > -8 d. $b$ > 8

#### Solution:

-6b > 48
[Original inequality.]

-6b-6 < 48-6
[Divide each side by -6 and reverse the inequality symbol.]

b < -8
[Simplify.]

9.
Solve the inequality - 7$k$ ≥ 56.
 a. $k$ ≥ - 8 b. $k$ ≤ - 8 c. $k$ ≥ 8 d. $k$ ≤ 8

#### Solution:

- 7k ≥ 56
[Original inequality.]

- 7k- 756- 7
[Divide each side by - 7 and reverse the inequality symbol.]

k ≤ - 8
[Simplify.]

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

#### Solution:

Let x be the cost of each dress.

As she can buy at most 3 dresses, the total cost of the 3 dresses is less than or equal to $150. 3x ≤ 150 [Write the inequality.] 3x31503 [Divide by 3 on each side.] x ≤ 50 [Simplify.] The maximum cost of each dress is$50.
[As x ≤ 50, the maximum value of x is 50.]