Understanding Compound Inequalities

This video tutorial by Mr. J covers compound inequalities, including graphing them on a number line, writing them from a number line, and solving them. The tutorial is divided into sections, each focusing on different aspects of compound inequalities, such as 'or' and 'and' inequalities. The video provides step-by-step examples to help viewers understand how to graph, write, and solve compound inequalities, and concludes with a section that combines solving and graphing.

What does a filled circle on a number line indicate when graphing inequalities?

• The inequality is an 'and' type.

• The inequality is an 'or' type.

• The number is included in the solution.

• The number is not included in the solution.

How can you identify an 'or' compound inequality from a number line?

• The inequalities are written without the word 'and'.

• The inequalities overlap.

• There is a gap between the inequalities.

• The inequalities are written without the word 'or'.

When solving 'or' compound inequalities, what is the key condition for a solution?

• The inequalities must overlap.

• Neither inequality can be true.

• At least one inequality must be true.

• Both inequalities must be true.

What happens to the inequality symbol when both sides are multiplied or divided by a negative number?

• The inequality symbol remains the same.

• The inequality symbol is removed.

• The inequality symbol becomes an equal sign.

• The inequality symbol flips direction.

In an 'and' compound inequality, what must be true for a number to be a solution?

• It must be greater than both inequalities.

• It must not satisfy either inequality.

• It must satisfy both inequalities.

• It must satisfy at least one inequality.

How can 'and' compound inequalities be written without using the word 'and'?

• By using a single inequality symbol.

• By placing the variable between the two inequalities.

• By using the word 'or' instead.

• By writing each inequality separately.

What is the first step in solving a compound inequality involving division?

• Multiply both sides by the same number.

• Divide both sides by the same number.

• Subtract the same number from both sides.

• Add the same number to both sides.

When graphing the solution of a compound inequality, what does an open circle represent?

• The inequality is an 'or' type.

• The number is not included in the solution.

• The inequality is an 'and' type.

• The number is included in the solution.

What is the result of solving the inequality 4c - 5 > -9 and < 7?

• c < -1 or c > 3

• c > -1 or c < 3

• c < -1 and c > 3

• c > -1 and c < 3

In the context of compound inequalities, what does it mean for two inequalities to overlap?

• They are solved separately.

• They share at least one common solution.

• They are graphed on different number lines.

• They have no common solutions.