Compound Inequalities

Front

What is a compound inequality?

Back

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

Front

What does 'x > 2 or x ≤ -3' represent?

Back

It represents two separate conditions: x is greater than 2 or x is less than or equal to -3.

Front

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

Back

First, solve each inequality separately: -4x ≤ 20 (x ≥ -5) and 5x < 20 (x < 4). The solution set is x ≥ -5 and x < 4.

Front

What is interval notation for '-8 ≤ x < 8'?

Back

The interval notation is [-8, 8).

Front

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

Back

Graph two separate regions: an open circle at 2 extending to the right, and a closed circle at -3 extending to the left.

Front

What does the solution 'All real numbers' mean in the context of inequalities?

Back

It means that any value of x satisfies the inequality.

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 express 'x < 4' in interval notation?

Back

The interval notation is (-∞, 4).

Front

What does the graph of '[-2, 5]' look like?

Back

It includes all numbers from -2 to 5, with -2 and 5 included (closed circles at both ends).

Front

What is the solution set for '5x + 1 < 21 OR 3x + 2 > -1'?

Back

The solution set is all real numbers.