linear inequality

Question 1

What is a linear inequality?

Answer 1

A linear inequality is a mathematical expression that shows the relationship between two expressions using inequality symbols.

Question 2

Which symbols are commonly used in linear inequalities?

Answer 2

The symbols are < (less than), > (greater than), ≤ (less than or equal to), and ≥ (greater than or equal to).

Question 3

True or False: The solution to a linear inequality can be a range of values.

Answer 3

True

Question 4

What is the general form of a linear inequality in one variable?

Answer 4

The general form is ax + b < c, ax + b > c, ax + b ≤ c, or ax + b ≥ c.

Question 5

Fill in the blank: When graphing a linear inequality, a dashed line indicates __________.

Answer 5

that the points on the line are not included in the solution.

Question 6

What do you do when you multiply or divide both sides of a linear inequality by a negative number?

Answer 6

You must reverse the inequality symbol.

Question 7

What is the solution set of the inequality 2x + 3 < 7?

Answer 7

x < 2

Question 8

Which of the following is the solution to the inequality x + 4 ≥ 10? A) x < 6 B) x = 6 C) x ≥ 6 D) x ≤ 6

Answer 8

C) x ≥ 6

Question 9

True or False: The solution to a linear inequality can be represented on a number line.

Answer 9

True

Question 10

What does the inequality x > 5 represent on a number line?

Answer 10

All numbers greater than 5, not including 5.

Question 11

Fill in the blank: The solution to the inequality -3x < 9 is __________.

Answer 11

x > -3

Question 12

How do you solve the inequality 5x - 2 ≥ 3?

Answer 12

Add 2 to both sides, then divide by 5: x ≥ 1.

Question 13

What is the graphical representation of the inequality y < 2x + 3?

Answer 13

A region below the line y = 2x + 3, with a dashed line.

Question 14

What type of line is used to represent ≤ and ≥ inequalities when graphed?

Answer 14

A solid line.

Question 15

True or False: Linear inequalities can have more than one variable.

Answer 15

True

Question 16

What is the solution to the system of inequalities: x + y < 4 and x - y > 1?

Answer 16

The region satisfying both inequalities on a graph.

Question 17

Which inequality symbol should be used to indicate ‘at least’?

Answer 17

≥ (greater than or equal to)

Question 18

Fill in the blank: The inequality 4x - 1 > 7 can be solved to find that x __________.

Answer 18

x > 2

Question 19

What does the solution x < 0 represent?

Answer 19

All negative numbers.

Question 20

What is the first step to solve the inequality 3(x + 2) ≤ 12?

Answer 20

Distribute 3 to both terms in the parentheses.

Question 21

True or False: Inequalities can be combined to form compound inequalities.

Answer 21

True

Question 22

What is the compound inequality for ‘x is between 2 and 5’?

Answer 22

2 < x < 5

Question 23

How do you express the inequality 3x + 4 > 10 in terms of x?

Answer 23

x > 2

Question 24

What does the inequality x - 1 ≤ 3 represent?

Answer 24

x is less than or equal to 4.

Question 25

Fill in the blank: The graph of x < 3 is represented by a __________ line.

Answer 25

dashed