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Website for Solving Absolute Value Inequalities

http://algebralab.net/lessons/lesson.aspx?file=Algebra_AbsoluteValueInequalities.xml

Solve Absolute Value Inequalities

Compound Inequalities

AND Compound Inequalities

Compound inequalities that contain the word and are true only if both inequalities are true. The graph of a compound inequality containing and is the intersection of the graphs of the two inequalities that make up the compound inequality. To find the intersection, determine where the two graphs overlap.

OR Compound Inequalities

Compound inequalities that contain the word or are true if one or more of the inequalities is true. The graph is the union of the graphs of the two inequalities that make up the compound inequality.

Solving Compound Inequalities (AND)

Solving Compound Inequalities (OR)

Inequality RULE

When multiplying or dividing both sides of an inequality by a negative number, you must reverse the inequality symbol.

Solving Inequalities

Example: Solve absolute value equations

Solve | 2x – 3 | – 4 = 3

First, I'll isolate the absolute-value part; that is, I'll get the absolute-value expression by itself on one side of the "equals" sign, with everything else on the other side:

| 2x – 3 | – 4 = 3
| 2x – 3 | = 7

Now I'll clear the absolute-value bars by splitting the equation into its two cases, one for each sign:

(2x – 3) = 7 or –(2x – 3) = 7
2x – 3 = 7 or –2x + 3 = 7
2x = 10 or –2x = 4
x = 5 or x = –2

So the solution is x = –2, 5.

Algebra 2: Solving Absolute Value Equation