Solving 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 '>' mean in an inequality?

Back

The symbol '>' means 'greater than'. For example, x > 3 means x is any number greater than 3.

Front

What does the symbol '<' mean in an inequality?

Back

The symbol '<' means 'less than'. For example, x < 5 means x is any number less than 5.

Front

What does the symbol '≥' mean in an inequality?

Back

The symbol '≥' means 'greater than or equal to'. For example, x ≥ 2 means x is any number greater than or equal to 2.

Front

What does the symbol '≤' mean in an inequality?

Back

The symbol '≤' means 'less than or equal to'. For example, x ≤ 4 means x is any number less than or equal to 4.

Front

How do you graph a linear inequality?

Back

To graph a linear inequality, first graph the corresponding linear equation as a dashed or solid line, then shade the region that represents the solution set based on the inequality symbol.

Front

What is the solution set of the inequality x < 3?

Back

The solution set of the inequality x < 3 includes all real numbers less than 3.

Front

What is the solution set of the inequality x ≥ -1?

Back

The solution set of the inequality x ≥ -1 includes all real numbers greater than or equal to -1.

Front

Given the inequality x < 4, which of the following numbers is NOT in the solution set? -1, 0, 4, 3

Back

4 is NOT in the solution set because x must be less than 4.

Front

Given the inequality x ≥ -2, which of the following numbers IS in the solution set? -3, -2, -1, -4

Back

-2 is in the solution set because x can be equal to -2.