Linear Inequalities

Front

What is a linear inequality?

Back

A linear inequality is a mathematical statement that compares a linear expression to a value using inequality symbols such as <, >, ≤, or ≥.

Front

What does the symbol '<' indicate in a linear inequality?

Back

The symbol '<' indicates that the value on the left is less than the value on the right.

Front

What does the symbol '>' indicate in a linear inequality?

Back

The symbol '>' indicates that the value on the left is greater than the value on the right.

Front

What does the symbol '≤' indicate in a linear inequality?

Back

The symbol '≤' indicates that the value on the left is less than or equal to the value on the right.

Front

What does the symbol '≥' indicate in a linear inequality?

Back

The symbol '≥' indicates that the value on the left is greater than or equal to the value on the right.

Front

How do you represent the solution set of a linear inequality on a number line?

Back

The solution set is represented by shading the region of the number line that satisfies the inequality, with an open circle for < or > and a closed circle for ≤ or ≥.

Front

What is the difference between a solid line and a dashed line when graphing inequalities?

Back

A solid line is used for inequalities with ≤ or ≥, indicating that points on the line are included in the solution set. A dashed line is used for < or >, indicating that points on the line are not included.

Front

How do you solve the inequality x < 3?

Back

To solve x < 3, you identify all values of x that are less than 3. The solution set is (-∞, 3).

Front

Which point is part of the solution set for the inequality x ≥ -2?

Back

Any point greater than or equal to -2, such as (-2, 0) or (0, 0), is part of the solution set.

Front

What is the solution to the inequality x > 0?

Back

The solution to x > 0 is all positive numbers, represented as (0, ∞).