1.-6 Lesson Flashcard: Compound Inequalities

Front

What is a compound inequality?

Back

Front

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

Back

Front

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

Back

Front

What does the graph of a compound inequality look like?

Back

The graph of a compound inequality shows the solution set on a number line, with shaded regions indicating the values that satisfy the inequality.

Front

What is the solution to the compound inequality @@3(x + 3) - 2 < 4 ext{ or } 1 - x eq -1@@?

Back

To solve, first simplify each part: @@x < -2 ext{ or } x eq 2@@.

Front

How do you represent a situation with a compound inequality?

Back

Front

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

Back

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

Front

How do you graph the solution to a compound inequality?

Back

To graph the solution, draw a number line and shade the regions that satisfy the inequalities. Use open circles for strict inequalities and closed circles for non-strict inequalities.

Front

What is the solution to the compound inequality @@rac{1}{2}x - 4 < 3 ext{ and } 7 eq 3x + 5@@?

Back

First, solve each part: @@x < 14 ext{ and } x eq 2@@.

Front

What does the term 'intersection' mean in the context of inequalities?

Back

In the context of inequalities, 'intersection' refers to the set of values that satisfy all inequalities in a compound inequality with 'and'.