Inequalities and Graphs Check

Front

What is an inequality in mathematics?

Back

An inequality is a mathematical statement that compares two expressions and shows that one is greater than, less than, greater than or equal to, or less than or equal to the other.

Front

What are the symbols used to represent inequalities?

Back

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

Front

How do you graph a linear inequality?

Back

To graph a linear inequality, first graph the corresponding equation as a line. Then, use a dashed line for < or > and a solid line for ≤ or ≥. Finally, shade the appropriate region based on the inequality.

Front

What does it mean to solve an inequality?

Back

Solving an inequality means finding all values of the variable that make the inequality true.

Front

What is the difference between a strict and a non-strict inequality?

Back

A strict inequality uses < or >, while a non-strict inequality uses ≤ or ≥, which includes the boundary value.

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 can you check if a value is a solution to an inequality?

Back

To check if a value is a solution, substitute it into the inequality and see if the statement is true.

Front

What is a compound inequality?

Back

A compound inequality combines two or more inequalities, often using 'and' or 'or' to connect them.

Front

What does it mean for a graph to represent an inequality?

Back

A graph representing an inequality shows all the possible solutions to that inequality on a number line or coordinate plane.

Front

What is the significance of the boundary line in graphing inequalities?

Back

The boundary line indicates the values where the inequality changes from true to false; it is included or excluded based on the type of inequality.