Understanding Compound Inequalities

In this video, Mr. J explains how to graph compound inequalities involving 'and' on a number line. He demonstrates how to write these inequalities without using the word 'and' and provides a visual representation by graphing them. The video includes examples to illustrate which numbers satisfy the compound inequality, emphasizing the need for solutions to meet both conditions of the inequality.

What is a compound inequality?

• An inequality with only one condition

• An inequality that has no solution

• An inequality that only uses the 'or' condition

• An inequality that combines two or more inequalities

How can a compound inequality involving 'and' be written without using the word 'and'?

• By writing each inequality on a separate line

• By using a comma between the inequalities

• By placing the variable in the middle of the two conditions

• By using the word 'or' instead

When graphing X > -2, what type of circle is used at -2?

• No circle is used

• A filled circle

• A half-filled circle

• An open circle

What direction does the arrow point when graphing X > -2?

• Right

• Up

• Left

• Down

When graphing X ≤ 7, what type of circle is used at 7?

• No circle is used

• A half-filled circle

• An open circle

• A filled circle

What direction does the arrow point when graphing X ≤ 7?

• Left

• Right

• Up

• Down

What is the solution set for the compound inequality X > -2 and X ≤ 7?

• All numbers less than or equal to 7

• All numbers between -2 and 7, including 7

• All numbers between -2 and 7, excluding both

• All numbers greater than -2

Which of the following numbers is a solution to the compound inequality X > -2 and X ≤ 7?

• -3

• 8

• 3

• 10

Why is 10 not a solution to the compound inequality X > -2 and X ≤ 7?

• Because 10 is not a number

• Because 10 is equal to 7

• Because 10 is greater than 7

• Because 10 is less than -2

What does the overlap of the two graphs represent in a compound inequality involving 'and'?

• The difference between the two inequalities

• The union of the two inequalities

• The sum of the two inequalities

• The intersection of the two inequalities