Solving 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

How do you solve the compound inequality 3x + 2 < -4 or 4x + 4 > 24?

Back

x < -2 or x > 5.

Front

What does the symbol '≤' mean?

Back

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

Front

Can x = 3 be a solution to the inequality 6 < x + 5 ≤ 11?

Back

Yes, because 6 < 8 ≤ 11 is true.

Front

What is the solution to the compound inequality 24 > -3r > -9?

Back

-8 < r < 3.

Front

What does the symbol '≥' mean?

Back

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

Front

How do you graph the inequality p ≤ 50?

Back

Shade the area to the left of 50 on a number line, including 50.

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.

Front

Solve the inequality: 2x - 3 > 5.

Back

x > 4.

Front

What is the solution set for the inequality x + 4 < 10?

Back

x < 6.