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?

Back

The symbol '≤' means 'less than or equal to.' It indicates that a value can be less than or equal to another value.

Front

What does the symbol '≥' mean?

Back

The symbol '≥' means 'greater than or equal to.' It indicates that a value can be greater than or equal to another value.

Front

How do you graph a linear inequality on a number line?

Back

To graph a linear inequality on a number line, use an open circle for < or > and a closed circle for ≤ or ≥. Shade the region that satisfies the inequality.

Front

What is the solution set of an inequality?

Back

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

Front

What happens to the inequality sign when you multiply or divide by a negative number?

Back

When you multiply or divide both sides of an inequality by a negative number, you must flip the inequality sign.

Front

Solve the inequality: -2x ≥ 22. What is x?

Back

x ≤ -11.

Front

Solve the inequality: x + 6 > 10. What is x?

Back

x > 4.

Front

What does it mean if an inequality has no solution?

Back

An inequality has no solution if there are no values that satisfy the inequality, often represented by a contradiction.

Front

What is a compound inequality?

Back

A compound inequality combines two or more inequalities, often connected by 'and' or 'or'.