Lesson 2.8---Solving Compound
Inequalities and Absolute Value Equations
Solve Compound inequalities
Write and solve absolute­value equations
A compound statement is made up of more than one
equation or inequality.
A disjunction is a compound statement that uses the word
or.
Disjunction: x ≤ –3 OR x > 2
Set builder notation: {x|x ≤ –3 U x > 2}
A disjunction is true if and only if at least one of its
parts is true.
A conjunction is a compound statement that uses the word and.
Conjunction: x ≥ –3 AND x < 2
Set builder notation: {x|x ≥ –3
x < 2}.
A conjunction is true if and only if all of its parts are true.
Conjunctions can be written as a single statement as shown.
–3 ≤ x < 2
x ≥ –3 and x< 2
1
Example:
Solve the compound inequality. Then graph the solution set.
Recall that the absolute value of a number x, written
distance from x to zero on the number line.
, is the
Because absolute value represents distance without regard to
direction, the absolute value of any real number is nonnegative.
2
Absolute­value equations can be represented by compound statements. Consider the equation |x| = 3.
The solutions of |x| = 3 are the two points that are 3 units from zero. The solution is a disjunction: x = –3 or x = 3.
Example:
Solve the equation.
|6x| – 8 = 22
.
3
Solve. Then graph the solution.
2. –7x < 21 and x + 7 ≤ 6
1. y – 4 ≤ –6 or 2y >8
Solve each equation.
3. |2v + 5| = 9
4. |5b| – 7 = 13
HW: p. 154 14­19, 28­35, 37, 38, 49, 55, 57 = 19 problems
4