Compound Inequalities

Front

What is a compound inequality?

Back

A compound inequality combines two or more inequalities using 'and' or 'or'.

Front

What does the inequality x > 2 or x ≤ -3 represent?

Back

It represents all values of x that are either greater than 2 or less than or equal to -3.

Front

How do you graph the compound inequality x > 2 or x ≤ -3?

Back

Graph a number line with an open circle at 2 (not including 2) and shade to the right, and a closed circle at -3 (including -3) and shade to the left.

Front

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

Back

The solution set is x ≥ -5 and x < 4.

Front

What does the notation [-2, 5] mean in interval notation?

Back

It means all numbers x such that -2 ≤ x ≤ 5, including -2 and 5.

Front

Which compound inequality results in no solution?

Back

x < 1 and x > 5 results in no solution because no number can be both less than 1 and greater than 5.

Front

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

Back

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

Front

How do you solve the compound inequality 2 < x < 5?

Back

The solution is all x such that 2 < x < 5, which can be written in interval notation as (2, 5).

Front

What is the graphical representation of the inequality x ≤ 3?

Back

A number line with a closed circle at 3 and shading to the left.

Front

What does the solution x > 1 or x < -1 look like on a number line?

Back

It shows an open circle at 1 and -1 with shading to the right of 1 and to the left of -1.