Final Midterm Review

Front

What is an identity inequality?

Back

An identity inequality is an inequality that is true for all values of the variable involved. For example, the inequality x + 2 > x is an identity inequality because it holds true for any value of x.

Front

How do you represent an identity inequality on a number line?

Back

An identity inequality is represented on a number line by shading the entire line, indicating that all values satisfy the inequality.

Front

What is a number line?

Back

A number line is a straight line that represents numbers as points at equal intervals. It is used to visualize numerical relationships and operations.

Front

What does it mean for an inequality to be true for all values?

Back

It means that no matter what value you substitute for the variable, the inequality will always hold true.

Front

What is the difference between an identity inequality and a conditional inequality?

Back

An identity inequality is true for all values of the variable, while a conditional inequality is only true for certain values.

Front

Can you give an example of a conditional inequality?

Back

An example of a conditional inequality is x > 3, which is only true for values of x that are greater than 3.

Front

What is the solution set of an inequality?

Back

The solution set of an inequality is the set of all values that satisfy the inequality.

Front

How do you find the solution set of a conditional inequality?

Back

To find the solution set of a conditional inequality, you determine the values of the variable that make the inequality true.

Front

What does it mean to graph an inequality?

Back

Graphing an inequality means representing the solution set on a number line or coordinate plane, showing all the values that satisfy the inequality.

Front

What is the significance of open and closed circles on a number line?

Back

An open circle indicates that the endpoint is not included in the solution set (e.g., x < 3), while a closed circle indicates that the endpoint is included (e.g., x ≤ 3).