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

What does 'and' mean in a compound inequality?

Back

In a compound inequality, 'and' means that both conditions must be true at the same time.

Front

What does 'or' mean in a compound inequality?

Back

In a compound inequality, 'or' means that at least one of the conditions must be true.

Front

Solve: 3x + 2 < -7 or -4x + 5 < 1

Back

x < -3 or x > 1

Front

What is the solution set for: -13 < 2x + 5 < 15?

Back

-9 < x < 5

Front

How do you graph a compound inequality with 'or'?

Back

Graph each inequality separately and shade the regions that satisfy either inequality.

Front

How do you graph a compound inequality with 'and'?

Back

Graph both inequalities on the same number line and shade the region where both inequalities overlap.

Front

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

Back

The solution includes all numbers greater than 2 and all numbers less than or equal to -3.

Front

What is the difference between strict and non-strict inequalities?

Back

Strict inequalities (<, >) do not include the boundary points, while non-strict inequalities (≤, ≥) do include them.

Front

Solve: 2x - 3 > 5 and x + 4 < 10

Back

x > 4 and x < 6, so the solution is 4 < x < 6.