1.7 Solve Absolute Value Equations and Inequalities Chapter 1 1.7 Solve Absolute Value Equations and Inequalities Prepared by Donald Danner

In this lesson you will: Solve absolute value expression and inequalities. Use absolute value equations and inequalites to solve real-life problems.

The absolute value of a number x (written |x| or abs(x)) Chapter 1 The absolute value of a number x (written |x| or abs(x)) Is the distance the number is from 0 on a number line. It is always a non-negative value. The distance between -4 and 0 is 4, so |-4|=4 The distance between 4 and 0 is 4, so |4|=4 What is the |0|=? Prepared by Donald Danner

Solving an Absolute Value Equation Chapter 1 Solving an Absolute Value Equation The absolute value equation |ax+b|=c, where c>0, is equivalent to the compound statement ax+b=c or ax+b=-c Prepared by Donald Danner

Solve |2x – 5| = 9 2x – 5 = 9 2x-5 = - 9 2x = 14 2x = -4 x = 7 x = -2 Chapter 1 Solve |2x – 5| = 9 And 2x – 5 = 9 2x-5 = - 9 2x = 14 2x = -4 x = 7 x = -2 Check these two solutions by substituting into the original equation. |2(7)-5|=|9|=9 |2(-2)-5|=|-9|=9 Prepared by Donald Danner

An absolute value inequality such as |x-1|<3 Chapter 1 An absolute value inequality such as |x-1|<3 Can be solved by rewriting it as a compound inequality -3 < x – 1 < 3 The solutions for x are any number between -2 and 4 not including the numbers -2 and 4…….Notice that is the numbers 3 units to the left of 1 and 3 units to the right of 1. -2 < x < 4 Prepared by Donald Danner

Solve |3x – 2| > 8 -8 > 3x – 2 > 8 -6 > 3x > 10 Chapter 1 Solve |3x – 2| > 8 -8 > 3x – 2 > 8 -6 > 3x > 10 -2 > x > 10/3 Carefully read what this is saying! As you can see, this is the same as the compound statement a x < -2 OR x > 10/3. Prepared by Donald Danner