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 solve the compound inequality x + 8 < 3 or -8x < -40?

Back

You solve each inequality separately: x + 8 < 3 gives x < -5, and -8x < -40 gives x > 5. The solution is x < -5 or x > 5.

Front

What symbols indicate a closed dot when graphing an inequality?

Back

The symbols ≤ (less than or equal to) and ≥ (greater than or equal to) indicate a closed dot.

Front

What does an open dot represent when graphing an inequality?

Back

An open dot represents that the endpoint is not included in the solution, used with the symbols < (less than) and > (greater than).

Front

Write the inequality represented by the graph with endpoints -2 and 5, including both endpoints.

Back

-2 ≤ x ≤ 5.

Front

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

Back

'And' means both conditions must be true simultaneously, while 'or' means at least one of the conditions must be true.

Front

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

Back

Graph two separate regions: one to the left of -5 with an open dot at -5, and one to the right of 5 with an open dot at 5.

Front

What is the solution set for the compound inequality 3 < x < 7?

Back

The solution set is all numbers between 3 and 7, not including 3 and 7.

Front

How do you express the solution of a compound inequality using interval notation?

Back

For the compound inequality x < -5 or x > 5, the interval notation is (-∞, -5) ∪ (5, ∞).

Front

What is the graphical representation of the inequality x ≥ 4?

Back

The graph includes a closed dot at 4 and a line extending to the right, indicating all numbers greater than or equal to 4.