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 express the compound inequality -8 ≤ x < 8 in interval notation?

Back

[-8, 8)

Front

What does the 'and' in a compound inequality signify?

Back

It means that both conditions must be true at the same time.

Front

What does the 'or' in a compound inequality signify?

Back

It means that at least one of the conditions must be true.

Front

What is the solution set for the inequality x < 1 and x > 5?

Back

No solution, because no number can be both less than 1 and greater than 5.

Front

How do you graph the compound inequality x < 1 or x > 5?

Back

Shade the regions to the left of 1 and to the right of 5 on a number line.

Front

What is the solution set for the inequality -8 < 2(x + 4) or -3x + 4 > x - 4?

Back

x < -8 or x < 2.

Front

How do you solve the compound inequality -4x + 1 ≤ 21 and 5x + 2 < 22?

Back

x ≥ -5 and x < 4.

Front

What is interval notation for the solution set x ≥ -5 and x < 4?

Back

[-5, 4)