Solving Inequalities with Addition and Subtraction Worksheet

**Page 1**

1.

Which of the graphs represents the inequality?

- 7.2 + $x$ ≤ - 3.3

- 7.2 + $x$ ≤ - 3.3

a. | Figure 1 | ||

b. | Figure 2 | ||

c. | Figure 3 | ||

d. | Figure 4 |

[Original inequality.]

- 7.2 +

[Add 7.2 to each side.]

[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.]

Correct answer : (1)

2.

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

a. | Graph 1 | ||

b. | Graph 2 | ||

c. | Graph 3 | ||

d. | Graph 4 |

Since the inequality involves less than (<), use dashed boundary line to graph the inequality

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

Correct answer : (4)

3.

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

a. | Graph 1 | ||

b. | Graph 2 | ||

c. | Graph 3 | ||

d. | Graph 4 |

Since the inequality involves less than (<), use dashed boundary line to graph the inequality

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

Correct answer : (1)

4.

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

a. | Graph 1 | ||

b. | Graph 2 | ||

c. | Graph 3 | ||

d. | Graph 4 |

Since the inequality involves less than (<), use dashed boundary line to graph the inequality

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

Correct answer : (2)

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 |

[Original inequality.]

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

[Add

Correct answer : (1)

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 |

[Original inequality.]

[Simplify.]

[Subtract 18 from each side.]

[Simplify.]

Jake should get atleast 8 in the fourth test.

Correct answer : (3)

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 |

[Given inequality.]

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

[Add

Correct answer : (2)

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 |

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

[Original inequality.]

[Add 292 to each side.]

[Simplify.]

Francis had at least $358 before he went shopping.

Correct answer : (1)

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 |

[Write an inequality.]

[Subtract 8 from each side.]

[Simplify.]

Andrew's present age is above 12 years.

Correct answer : (2)

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 |

[In words.]

Let

[Original Inequality.]

[Subtract 205 from each side.]

[Simplify.]

The other number is greater than 149.

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

So, 153 is the other number.

Correct answer : (4)