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)