Solving Compound Inequalities and Operations

In this video, Mr. J explains how to solve and graph compound inequalities. The tutorial covers two types of compound inequalities: 'or' and 'and'. For 'or' inequalities, each inequality is solved separately, and solutions are graphed on a number line. For 'and' inequalities, both inequalities are solved simultaneously, and the overlapping solutions are graphed. The video provides step-by-step instructions and examples for each type, helping viewers understand the process of solving and graphing compound inequalities.

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

• Solve both inequalities together.

• Combine the inequalities into one.

• Solve each inequality separately.

• Graph the inequalities first.

When solving the inequality -5W - 2/8 > -4, what operation should be used first?

• Division

• Multiplication

• Subtraction

• Addition

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

• It stays the same.

• It flips direction.

• It becomes an equal sign.

• It disappears.

In the inequality 2W + 6 > 30, what is the first step to isolate W?

• Multiply both sides by 2.

• Subtract 6 from both sides.

• Add 6 to both sides.

• Divide both sides by 2.

What is the solution set for the compound inequality W < 6 or W > 12?

• W is between 6 and 12.

• W is less than 6 or greater than 12.

• W is greater than 6 and less than 12.

• W is exactly 6 or 12.

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

• Graph the inequalities first.

• Solve each inequality separately.

• Ignore one of the inequalities.

• Solve both inequalities at the same time.

In the inequality 4C - 5 > -9 and < 7, what is the first step to isolate C?

• Subtract 5 from all parts of the inequality.

• Divide all parts by 4.

• Add 5 to all parts of the inequality.

• Multiply all parts by 4.

What is the solution set for the compound inequality C ≥ -1 and C < 3?

• C is exactly -1 or 3.

• C is greater than -1 and less than 3.

• C is between -1 and 3, including -1.

• C is less than -1 or greater than 3.

What type of circle is used on a number line to represent that a number is not included in the solution set?

• Filled circle

• Square

• Triangle

• Open circle

What does it mean when two inequalities overlap on a number line?

• The inequalities are equal.

• The solution is outside the overlap.

• The solution is where they overlap.

• There is no solution.