A compound inequality is an inequality that is linked with a connective word such as ‘and’ or ‘or’. The solution for a compound inequality with ‘and’ is the intersection of the two solutions sets. The solution for a compound inequality with ‘or’ is the union of the two solutions sets.
Test Objectives:•Demonstrate the ability to solve a compound inequality with "and"
•Demonstrate the ability to solve a compound inequality with "or"
•Demonstrate the ability to graph the solution for a compound inequality
Solving Compound Inequalities Test:
#1:
Instructions: Solve each inequality, write the solution in interval notation, and graph the interval.
a) 3r - 7 ≤ r + 7 and 11r + 7 > 6r - 3
#2:
Instructions: Solve each inequality, write the solution in interval notation, and graph the interval.
a) -2 - 12n ≤ -15n - 14 and 2n + 9 ≤ n + 2
#3:
Instructions: Solve each inequality, write the solution in interval notation, and graph the interval.
a) -2(6 - 7x) < 16 + 7x and 13x + 7 ≥ 12x + 13
#4:
Instructions: Solve each inequality, write the solution in interval notation, and graph the interval.
a) 2(2 + 4n) < -12 or 9n + 19 > 46
#5:
Instructions: Solve each inequality, write the solution in interval notation, and graph the interval.
a) 7 - 20v ≥ 67 or 8v + 9 ≥ -95
Written Solutions:
Solution:
a) -2 < r ≤ 7
(-2,7]
Solution:
a) n ≤ -7
(-∞,-7)
Solution:
a) No solution
∅
Solution:
a) n < -2 or n > 3
(-∞,-2) ∪ (3,∞)
Solution:
a) All real numbers
(-∞,∞)