CHAPTER 1 – EQUATIONS AND INEQUALITIES 1.4 – SOLVING ABSOLUTE VALUE EQUATIONS Unit 1 – First-Degree Equations and Inequalities

1.4 – Solving Absolute Value Equations In this section we will review:  Evaluating expression involving absolute values  Solving absolute value equations

1.4 – Solving Absolute Value Equations Absolute value – a number’s distance from zero on a number line  Since distance is nonnegative, the absolute value of a number is always nonnegative |x||x|

1.4 – Solving Absolute Value Equations Example 1  Evaluate |6 – 2x| if x = 4

1.4 – Solving Absolute Value Equations Some equations contain absolute value expressions  For any real numbers a and b, where b ≥ 0, if |a| = b, then a = b or a = -b.

1.4 – Solving Absolute Value Equations Example 2  Solve |y + 3| = 8. Check your solutions.

1.4 – Solving Absolute Value Equations Since the absolute value of a number is always positive or zero, an equation like |x| = -5 is never true.  Therefore it has no solution  The solution set is called the empty set

1.4 – Solving Absolute Value Equations Example 3  Solve |6 – 4t| + 5 = 0

1.4 – Solving Absolute Value Equations It is important to check your answers when solving absolute value problems.  Even if the correct procedure is used, the answers may not be solutions

1.4 – Solving Absolute Value Equations Example 4  Solve |8 + y| = 2y – 3. Check your solutions.

1.4 – Solving Absolute Value Equations HOMEWORK Page 29 #12-18 (even), #36-42 (even)