1. UNIT 4, LESSON 5 Absolute Value Equations

2. Review of Absolute Value http://www.brainpop.com/math/numbersandoperat ions/absolutevalue/preview.weml http://www.brainpop.com/math/numbersandoperat ions/absolutevalue/preview.weml

3. The absolute-value of a number is that numbers distance from zero on a number line. For example, |–5| = 5. 55 44 33 22 012345 66 11 6 5 units Both 5 and –5 are a distance of 5 units from 0, so both 5 and –5 have an absolute value of 5.

4. 1.Isolate the absolute-value expression 2.Split the problem into two cases. How to Solve Absolute Value Equations:

5. Solve the equation. |x| – 3 = 4 + 3 +3 |x| = 7 x = 7 –x = 7 –1(–x) = –1(7) x = –7

6. Solve |a| – 3 = 5 + 3 + 3 |a| = 8 a = 8 or a = –8 Example:

7. Solve the equation. |x  2| = 8 +2 x  2 = 8 x = 10 +2 x =  6 x  2 =  8

8. Solve |3c – 6| = 9 3c – 6 = 9 3c – 6 = –9 + 6 3c = 15 3 3 c = 5 Example: + 6 3c = –3 3 3 c = –1

9. |x + 7| = 8 x + 7 = 8 x + 7 = –8 – 7 –7– 7 x = 1 x = –15 3 3

10. Not all absolute-value equations have solutions. If an equation states that an absolute-value is negative, there are no solutions. CAREFUL!

11. Solve the equation. 2  |2x  5| = 7  2  |2x  5| = 5 Absolute values cannot be negative. |2x  5| =  5 This equation has no solution.  1