solving 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 a compound inequality with 'and'?

Back

To solve a compound inequality with 'and', find the intersection of the solution sets of the individual inequalities.

Front

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

Back

To solve a compound inequality with 'or', find the union of the solution sets of the individual inequalities.

Front

What does the inequality 2x + 10 ≤ 25 represent in a real-world context?

Back

It represents a situation where the total cost of games and food does not exceed $25.

Front

How do you graph the inequality -5 ≤ x < 0?

Back

Draw a number line, shade the region from -5 to 0, including -5 (closed dot) and excluding 0 (open dot).

Front

What is the solution to the compound inequality 2 ≤ x ≤ 4?

Back

The solution is all values of x that are greater than or equal to 2 and less than or equal to 4.

Front

What is the solution to the compound inequality -8 < 2(x + 4) or -3x + 4 > x - 4?

Back

The solution is x > -8 or x < 2.

Front

What does the graph of x ≤ -2 AND x > 5 look like?

Back

There are no values of x that satisfy both conditions simultaneously, so the graph is empty.

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 write an inequality for the graph that shows -2 ≤ x < 5?

Back

The inequality is -2 ≤ x < 5.