Compound Inequalities and Interval Notation

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 the interval notation (a, b) represent?

Back

The interval notation (a, b) represents all real numbers x such that a < x < b, meaning a and b are not included in the interval.

Front

What does the interval notation [a, b] represent?

Back

The interval notation [a, b] represents all real numbers x such that a ≤ x ≤ b, meaning a and b are included in the interval.

Front

What does the symbol U represent in interval notation?

Back

The symbol U represents the union of two intervals, meaning all numbers that are in either interval.

Front

How do you express the solution to the inequality x > 2 in interval notation?

Back

The solution x > 2 is expressed in interval notation as (2, ∞).

Front

How do you express the solution to the inequality x ≤ -3 in interval notation?

Back

The solution x ≤ -3 is expressed in interval notation as (-∞, -3].

Front

What is the difference between using ( ) and [ ] in interval notation?

Back

( ) indicates that the endpoint is not included (open interval), while [ ] indicates that the endpoint is included (closed interval).

Front

What is the solution to the compound inequality x > 2 or x ≤ -3?

Back

The solution is expressed in interval notation as (-∞, -3] U (2, ∞).

Front

How do you solve the inequality 3x + 2 < -7?

Back

To solve 3x + 2 < -7, subtract 2 from both sides to get 3x < -9, then divide by 3 to find x < -3.

Front

How do you solve the inequality -4x + 5 < 1?

Back

To solve -4x + 5 < 1, subtract 5 from both sides to get -4x < -4, then divide by -4 (remember to flip the inequality) to find x > 1.