Understanding Compound Inequalities

The video tutorial by Mr. J explains how to solve compound inequalities involving 'and'. It covers two examples, demonstrating both methods of solving: separately and together. The first example involves inequalities with 'x', while the second example uses 'm'. The tutorial emphasizes understanding and organizing the steps to isolate the variable and solve the inequalities effectively.

What is a compound inequality involving 'and'?

• An inequality that must satisfy at least one condition

• An inequality that must satisfy both conditions

• An inequality with no conditions

• An inequality that only involves addition

In the first example, what operation is used to isolate x in the inequality x - 6 ≥ 0?

• Subtraction

• Multiplication

• Addition

• Division

What is the solution for x in the inequality x - 6 ≤ 11?

• x ≤ 11

• x ≤ 5

• x ≤ 6

• x ≤ 17

When solving both inequalities simultaneously, what is the final solution for x?

• x ≥ 5 and x ≤ 17

• x ≥ 2 and x ≤ 11

• x ≥ 0 and x ≤ 11

• x ≥ 6 and x ≤ 17

In the second example, what is the first step to isolate m in the inequality 3m + 7 ≥ -2?

• Add 7 to both sides

• Subtract 7 from both sides

• Multiply both sides by 3

• Divide both sides by 3

What is the solution for m in the inequality 3m + 7 < 13?

• m < 6

• m < 3

• m < 2

• m < 1

What is the final solution for m when solving both inequalities separately in the second example?

• m ≥ -1 and m < 2

• m ≥ -2 and m < 3

• m ≥ -3 and m < 2

• m ≥ 0 and m < 3

When solving both inequalities simultaneously in the second example, what is the final solution for m?

• m ≥ -3 and m < 2

• m ≥ -2 and m < 3

• m ≥ -1 and m < 2

• m ≥ 0 and m < 3

What operation is used to isolate m in the inequality 3m < 6?

• Division

• Multiplication

• Subtraction

• Addition

What is the key takeaway from solving compound inequalities involving 'and'?

• The conditions are irrelevant

• No conditions need to be true

• Both conditions must be true

• Only one condition needs to be true