Absolute Value Equations and Inequalities Lesson 1-5 Absolute Value Equations and Inequalities

Absolute Value – distance a number is from zero. Can distance ever be negative? Since distance is always nonnegative, absolute values are always positive.

Steps to solve absolute value equations If necessary get the absolute value by itself on the left side. Drop the absolute value symbols and write an or statement. Make the right side negative on the second statement Solve each statement Check your answer in the original problem

|2y – 4| = 12 2|3x – 1| + 5 = 33

Extraneous solution – solution of an equation derived from an original equation that is not a solution of the original equation.

Check for extraneous solutions |2x + 5| = 3x + 4

Solving Absolute Value Inequalities Get the absolute value by itself on the left side Determine whether it is an and or an or statement Write the correct statement and solve Graph

|A| ≥ b If the absolute value is alone on the left side and the symbol is greater than (>,≥) write the inequality in OR form. NOTE on the negative you must flip the sign NOTE: For an OR statement- if there is a negative number alone on the right side the answer will be ALL REAL NUMBERS

Solve |2x – 3| > 7

If the absolute value is alone on the left side and the symbol is less than (<,≤) write the inequality in AND form. NOTE: For an AND statement - if there is a negative number alone on the right side the answer will be NO SOLUTION

Solve 3|2x + 6| - 9 < 15

Summary Absolute Value Inequalities |x| ≥ k is equivalent to x ≤ -k or x ≥ k |x| ≤ k is equivalent to -k ≤ x ≤ k

Assignment 2-26 even and 34 – 50 even on pgs 36 - 37