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

How do you solve the compound inequality -13 < 2x + 5 < 15?

Back

First, isolate x: -18 < 2x < 10, then divide by 2: -9 < x < 5.

Front

What is the solution set for the inequality -3 ≤ 2x - 1 ≤ 5?

Back

The solution set is -1 ≤ x ≤ 3.

Front

When do you use an open dot on a graph of an inequality?

Back

An open dot is used for inequalities with '<' or '>'.

Front

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

Back

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

Front

What does the compound inequality 2 ≤ x ≤ 4 represent on a number line?

Back

It represents all values of x that are between 2 and 4, inclusive.

Front

How do you graph the inequality x < 3?

Back

Draw a number line, place an open dot at 3, and shade to the left.

Front

What is the difference between 'and' and 'or' in compound inequalities?

Back

'And' means both conditions must be true, while 'or' means at least one condition must be true.