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' means 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' means 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 solutions.

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 solutions.

Front

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

Back

x ≥ -5 and x < 4.

Front

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

Back

Graph the solution of each inequality on the same number line and shade the region where they overlap.

Front

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

Back

Graph the solution of each inequality on the same number line and shade all regions that satisfy either inequality.

Front

What is the inequality that models the taxi fare scenario: $2.50 per mile plus a $5 fee with a $20 budget?

Back

2.50x + 5 ≤ 20.

Front

What is the solution to the inequality 2.50x + 5 ≤ 20?

Back

x ≤ 6.