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

Solve the compound inequality: 3 < x + 2 < 5.

Back

0 < x < 3.

Front

What does it mean to graph an inequality?

Back

Graphing an inequality visually represents all the solutions to the inequality on a number line.

Front

Solve the absolute value inequality: |2x - 1| = 7.

Back

x = -3 or x = 4.

Front

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

Back

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

Front

Write the compound inequality for the graph that shows x ≤ -2 or x > 5.

Back

x ≤ -2 OR x > 5.

Front

How do you solve an absolute value inequality like |x + 3| < 5?

Back

Split it into two inequalities: -5 < x + 3 < 5, then solve for x.

Front

What is the solution set for the inequality 2x - 4 > 6?

Back

x > 5.

Front

How do you represent the solution of a compound inequality on a number line?

Back

Use open or closed circles to indicate whether endpoints are included, and shade the region that satisfies the inequality.

Front

What is the solution to the inequality 5 < 2x + 1 < 11?

Back

2 < x < 5.