Understanding Compound Inequalities

What is a compound inequality?

• An equation with one variable

• Two or more inequalities connected by 'and' or 'or'

• A single inequality with no connections

• An equation with two variables

When is a compound inequality containing 'and' true?

• When at least one inequality is true

• When both inequalities are false

• When neither inequality is true

• When both inequalities are true

How do you graph the solution set for x ≥ 4 and x < 7?

• Closed circle at 4, open circle at 7, shade in between

• Open circle at 4, closed circle at 7, shade in between

• Closed circle at 4, closed circle at 7, shade outside

• Open circle at 4, open circle at 7, shade outside

What is the solution set for 7 < z + 2 and z + 2 ≤ 11?

• z > 5 and z ≤ 9

• z < 5 and z ≥ 9

• z ≤ 5 and z > 9

• z ≥ 5 and z < 9

What is the intersection of the graphs for z > 5 and z ≤ 9?

• Open circle at 5, closed circle at 9, shade in between

• Closed circle at 5, open circle at 9, shade in between

• Open circle at 5, open circle at 9, shade outside

• Closed circle at 5, closed circle at 9, shade outside

When is a compound inequality containing 'or' true?

• When both inequalities are true

• When at least one inequality is true

• When neither inequality is true

• When both inequalities are false

How do you graph the solution set for x > 3 or x ≤ 1?

• Open circle at 3, closed circle at 1, shade outside

• Closed circle at 3, open circle at 1, shade in between

• Open circle at 3, open circle at 1, shade in between

• Closed circle at 3, closed circle at 1, shade outside

What is the solution set for 4k - 7 ≤ 25 or 12 - 9k ≥ 30?

• k > 8 or k < -2

• k < 8 or k > -2

• k ≥ 8 or k ≤ -2

• k ≤ 8 or k ≥ -2

What does the graph of k ≤ 8 or k ≤ -2 look like?

• Closed circle at 8, closed circle at -2, shade outside

• Open circle at 8, open circle at -2, shade in between

• Closed circle at 8, closed circle at -2, shade in between

• Open circle at 8, closed circle at -2, shade outside

What is the union of the graphs for k ≤ 8 and k ≤ -2?

• Neither graph includes the other

• The graph of k ≤ 8 includes k ≤ -2

• The graph of k ≤ -2 includes k ≤ 8

• Both graphs are separate