7.3 COMPOUND INEQUALITIES
AND INTERVAL NOTATION
Review
 Inequality – sentence containing <,>,≤,≥,≠
 Solution – that which makes the statement
true
 Explanation of open and closed brackets,
parentheses, and circles
Solving Inequalities


Same steps for solving equations except when
dividing or multiplying through by a negative
number
You must remember to reverse the inequality sign
to maintain the integrity of the original problem
Case 1: 3 < 7
Case 2: 3 < 7
3(2) < 7(2)
3(-2) < 7(-2)
6 < 14 TRUE
-6 < -14 FALSE
Reversing the sign would solve the problem -6 > -14


This will almost always occur at the last step of the
problem
Always graph the translation on a number line to
translate to interval notation
Example
Solve the inequality.
-9x + 3x ≥ -24
-6x ≥ -24
x≤4
Set Notation: {x | x ≤4}
Graph Notation: Number line
Interval Notation: {-∞, 4]
Examples
Solve. Graph each solution and write in interval
notation
1. -2/3x < -8
2. 9/5 > -1/5 – 1/2x
3. 1 ≥ 3 – 4(3a - 1)
Compound Inequalities
 Consist of 2 or more inequalities to be solved
simultaneously
 And: means the intersection of the solutions;
looking for the overlap
 Or: means the union of the solutions; join the two
solutions
 Always graph the individual solutions to see
what the intersection or union looks like
Examples
Solve and write the solution using interval
notation
1. -2 < x + 4 < 7
2. 4x – 7 < 1 and 7-3x > -8
3. X – 5 ≤ -4 or 2x – 7 ≥ 3
4. 3x + 2 < 2 or 4 – 2x < 14