Solving Compound Inequalities Effectively

What must you do to the inequality sign when you multiply or divide by a negative number?

• Keep it the same

• Flip it

• Add 1 to it

• Subtract 1 from it

In the first example, what is the solution set for the inequality n ≤ -4 or n > 2?

• n ≤ -4 or n > 2

• n ≥ -4 or n < 2

• n ≤ -4 and n > 2

• n ≥ -4 and n < 2

How do you graph the solution n ≤ -4 or n > 2?

• Closed circle at -4, open circle at 2, shade between

• Open circle at -4, closed circle at 2, shade outside

• Open circle at -4, closed circle at 2, shade between

• Closed circle at -4, open circle at 2, shade outside

In the second example, how is the solution set written for the inequality 1 ≤ X ≤ 7?

• 1 ≥ X ≥ 7

• 1 ≤ X ≤ 7

• X ≤ 1 and X ≥ 7

• X ≥ 1 or X ≤ 7

What does the graph look like for the solution 1 ≤ X ≤ 7?

• Closed circles at 1 and 7, shade outside

• Open circles at 1 and 7, shade between

• Closed circles at 1 and 7, shade between

• Open circles at 1 and 7, shade outside

In the complex example, what is the solution set for the inequality B ≥ 12 or B < -8?

• B ≤ 12 and B > -8

• B ≥ 12 or B < -8

• B ≤ 12 or B > -8

• B ≥ 12 and B < -8

How do you graph the solution B ≥ 12 or B < -8?

• Open circle at 12, closed circle at -8, shade between

• Closed circle at 12, open circle at -8, shade between

• Open circle at 12, closed circle at -8, shade outside

• Closed circle at 12, open circle at -8, shade outside

What is the solution set for the inequality -11 ≤ X ≤ -5?

• X ≥ -11 and X ≤ -5

• X ≤ -11 or X ≥ -5

• X ≥ -11 or X ≤ -5

• X ≤ -11 and X ≥ -5

How do you graph the solution -11 ≤ X ≤ -5?

• Closed circles at -11 and -5, shade outside

• Open circles at -11 and -5, shade between

• Closed circles at -11 and -5, shade between

• Open circles at -11 and -5, shade outside

What is the result when there is no overlap in an 'and' statement?

• One solution

• No solution

• Infinite solutions

• Two solutions