Inequalities

Question 1

What are inequalities in mathematics?

Answer 1

In mathematics, inequalities are expressions that show the relative size or order of two values, indicating that one value is less than, greater than, less than or equal to, or greater than or equal to another.

Question 2

What is the symbol for “less than”?

Answer 2

The symbol for “less than” is “<”. For example, if x < 5, it means x is less than 5.

Question 3

What does “greater than or equal to” mean?

Answer 3

The symbol “≥” represents “greater than or equal to,” indicating that a value can be either greater than or equal to another value.

Question 4

How do you solve linear inequalities?

Answer 4

To solve linear inequalities, isolate the variable on one side of the inequality sign using similar steps as solving equations, while remembering to reverse the inequality sign if multiplying or dividing by a negative number.

Question 5

What is a compound inequality?

Answer 5

A compound inequality consists of two or more inequalities joined by the words “and” or “or,” representing a range of values that satisfy the conditions.

Question 6

What is the solution set for inequality?

Answer 6

The solution set of an inequality is the set of all values that make the inequality true. This can be expressed in interval notation or on a number line.

Question 7

How do you graph inequalities on a number line?

Answer 7

To graph inequalities on a number line, use an open circle for “<” or “>” (not including the endpoint) and a closed circle for “≤” or “≥” (including the endpoint), then shade the appropriate direction.

Question 8

What are absolute value inequalities?

Answer 8

Absolute value inequalities involve expressions that contain absolute values, representing the distance from zero. They can be solved by creating two separate inequalities: one for the positive case and one for the negative case.