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 'and' mean in a compound inequality?

Back

In a compound inequality, 'and' indicates that both conditions must be true at the same time.

Front

What does 'or' mean in a compound inequality?

Back

In a compound inequality, 'or' indicates that at least one of the conditions must be true.

Front

How do you solve a compound inequality with 'and'?

Back

To solve a compound inequality with 'and', solve each inequality separately and find the intersection of the solution sets.

Front

How do you solve a compound inequality with 'or'?

Back

To solve a compound inequality with 'or', solve each inequality separately and find the union of the solution sets.

Front

What is interval notation?

Back

Interval notation is a way of writing subsets of the real number line using intervals, such as (a, b) or [a, b].

Front

What does the symbol '≤' mean?

Back

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

Front

What does the symbol '≥' mean?

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

Front

How do you graph a compound inequality?

Back

To graph a compound inequality, shade the regions that satisfy the inequality on a number line.

Front

What is the solution set of the inequality -4x + 1 ≤ 21 and 5x + 2 < 22?

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The solution set is x ≥ -5 and x < 4.