Graphing Compound Inequalities

Front

What is a compound inequality?

Back

A compound inequality is an inequality that combines two or more simple inequalities using the words 'and' or 'or'.

Front

What does the symbol '≤' mean?

Back

The symbol '≤' means 'less than or equal to'.

Front

What does the symbol '≥' mean?

Back

The symbol '≥' means 'greater than or equal to'.

Front

When do you use an open dot on a graph?

Back

An open dot is used when the inequality symbol is '<' or '>' indicating that the endpoint is not included.

Front

When do you use a closed dot on a graph?

Back

A closed dot is used when the inequality symbol is '≤' or '≥' indicating that the endpoint is included.

Front

How do you solve the compound inequality 3x + 2 < -7 or -4x + 5 < 1?

Back

Solve each inequality separately: 3x < -9 (x < -3) and -4x < -4 (x > 1). The solution is x < -3 or x > 1.

Front

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

Back

The inequality sign must be flipped when you multiply or divide both sides by a negative number.

Front

What is the solution to the inequality 0 ≤ x < 5?

Back

The solution means x can take any value from 0 to 5, including 0 but not including 5.

Front

What is the graphical representation of the inequality -2 ≤ x ≤ 2?

Back

The graph includes a closed dot at -2 and 2, with a shaded line connecting them.

Front

What does the solution x < -3 or x > 1 represent on a number line?

Back

It represents two separate regions: all numbers less than -3 and all numbers greater than 1.