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 the compound inequality -3 ≤ 2x - 1 ≤ 5?

Back

Add 1 to all parts: -2 ≤ 2x ≤ 6. Then divide by 2: -1 ≤ x ≤ 3.

Front

What is the solution set for the inequality x + 8 < 3?

Back

x < -5.

Front

What is the solution set for the inequality -8x < -40?

Back

x > 5.

Front

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

Back

'And' requires both conditions to be satisfied, while 'or' requires at least one condition to be satisfied.

Front

How do you graph the compound inequality -2 ≤ x ≤ 5?

Back

Draw a number line, shade between -2 and 5, and use closed circles at -2 and 5.

Front

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

Back

x ≥ -5 and x < 4.

Front

What is the solution for the compound inequality x < -5 or x > 5?

Back

The solution set includes all numbers less than -5 and all numbers greater than 5.