﻿ Solving Inequalities with Addition and Subtraction Worksheet | Problems & Solutions

# Solving Inequalities with Addition and Subtraction Worksheet

Solving Inequalities with Addition and Subtraction Worksheet
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1.
Which of the graphs represents the inequality?
- 7.2 + $x$ ≤ - 3.3

 a. Figure 1 b. Figure 2 c. Figure 3 d. Figure 4

#### Solution:

- 7.2 + x ≤ - 3.3
[Original inequality.]

- 7.2 + x + 7.2 ≤ - 3.3 + 7.2

x ≤ 3.9
[Simplify.]

The solution for the inequality is the set of all real numbers less than or equal to 3.9.

So, among the choices, Figure 1 is the appropriate graph for the inequality.
[The set of numbers to the left of 3.9 is the solution for the inequality.]

2.
Which of the graphs best suits the inequality $y$ < $x$ - 2?

 a. Graph 1 b. Graph 2 c. Graph 3 d. Graph 4

#### Solution:

Since the inequality involves less than (<), use dashed boundary line to graph the inequality y < x - 2 as in the below shown graph.

y < x - 2
0 < 0 - 2
0 < - 2
Test a point, which is not on the boundary line.
Test (0, 0) in the inequality.
[Substitute.]

[False.]

Since the inequality is false for (0, 0), shade the region that does not contain (0, 0).

Therefore, Graph 4 best suits the inequality y < x - 2.

3.
Which of the graphs best suits the inequality $y$ < $x$ - 4?

 a. Graph 1 b. Graph 2 c. Graph 3 d. Graph 4

#### Solution:

Since the inequality involves less than (<), use dashed boundary line to graph the inequality y < x - 4 as in the below shown graph.

y < x - 4
0 < 0 - 4
0 < - 4
Test a point, which is not on the boundary line.
Test (0, 0) in the inequality.
[Substitute.]

[False.]

Since the inequality is false for (0, 0), shade the region that does not contain (0, 0).

Therefore, Graph 1 best suits the inequality y < x - 4.

4.
Which of the graphs best suits the inequality $y$ < $x$ + 4?

 a. Graph 1 b. Graph 2 c. Graph 3 d. Graph 4

#### Solution:

Since the inequality involves less than (<), use dashed boundary line to graph the inequality y < x + 4 as in the below shown graph.

y < x + 4
0 < 0 + 4
0 < 4
Test a point, which is not on the boundary line.
Test (0, 0) in the inequality.
[Substitute.]

[False.]

Since the inequality is false for (0, 0), shade the region that does not contain (0, 0).

Therefore, Graph 2 best suits the inequality y < x + 4.

5.
Which of the following is true, if $a$ > $b$?
 a. a + c > b + c b. a - c < b - c c. a + c < b + c d. None of the above

#### Solution:

a > b
[Original inequality.]

The inequality is not changed when the same quantity is added on each side.

a + c > b + c

6.
Jake had to appear for four Math tests each having the total score as 10. The scores he got in three tests are 8, 8 and 2. How many points should he score in his fourth test, to have a total of at least 26 in the four tests?
 a. atmost 7 b. atleast 13 c. atleast 8 d. atmost 8

#### Solution:

Let n be the score of Jake in the fourth test.

n + 8 + 8 + 2 ≥ 26
[Original inequality.]

n + 18 ≥ 26
[Simplify.]

n + 18 - 18 ≥ 26 - 18
[Subtract 18 from each side.]

n ≥ 8
[Simplify.]

Jake should get atleast 8 in the fourth test.

7.
Which of the following choice is true, if $a$ < $b$?
 a. a - c > b - c b. a + c < b + c c. a + c > b + c d. None of the above

#### Solution:

a < b
[Given inequality.]

The inequality is not changed when the same quantity is added to each side.

a + c < b + c

8.
Francis went shopping and spent $292. By the time he came back to his house, he had at least$66 in his pocket. How much did he have before he went shopping?
 a. At least 358 b. At most 424 c. 358 d. None of the above

#### Solution:

Let m be the amount Francis had in his pocket before he went shopping.

Money in Francis's pocket before shopping - Money spent ≥ Money left over

m - 292 ≥ 66
[Original inequality.]

m - 292 + 292 ≥ 66 + 292

m ≥ 358
[Simplify.]

Francis had at least \$358 before he went shopping.

9.
How old is Andrew now, if he will be above 20 after 8 years?
 a. 12 years b. Above 12 years c. Below 12 years d. None of the above

#### Solution:

Let a be the present age of Andrew.

a + 8 > 20
[Write an inequality.]

a + 8 - 8 > 20 - 8
[Subtract 8 from each side.]

a > 12
[Simplify.]

Andrew's present age is above 12 years.

10.
The sum of two numbers is more than 354. If one of the numbers is 205, then which of the following numbers can be the other number?
 a. 148 b. 146 c. 147 d. 153

#### Solution:

The sum of two numbers is more than 354.
[In words.]

Let x be the unknown number.

x + 205 > 354
[Original Inequality.]

x + 205 - 205 > 354 - 205
[Subtract 205 from each side.]

x > 149
[Simplify.]

The other number is greater than 149.

Among the choices, the number greater than 149 is 153.

So, 153 is the other number.