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 in an inequality?

Back

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

Front

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

Back

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

Front

When do you use an open dot on a number line?

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 number line?

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 -4x + 1 ≤ 21 and 5x + 2 < 22?

Back

The solution is x ≥ -5 and x < 4.

Front

What is the solution set for the compound inequality x > 2 or x ≤ -3?

Back

The solution set includes all values greater than 2 and all values less than or equal to -3.

Front

What is the solution to the compound inequality -3 ≤ 2x - 1 ≤ 5?

Back

The solution is -1 ≤ x ≤ 3.

Front

What does 'and' mean in a compound inequality?

Back

'And' means that both inequalities must be true at the same time.

Front

What does 'or' mean in a compound inequality?

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'Or' means that at least one of the inequalities must be true.