1. 1-6 Absolute Value and Distance Goal Recognize the connections between absolute value and distance, and the implications the definition of absolute value has for distinguishing x from |x|. Big Idea The absolute value of a # and the distance between 2 #s on a # line are closely related.

2. The _____________________ on a number line is: | x - x | 2 1 distance between 2 points The ___________ of a _______ its ___________. absolute valuenumber is distance from 0

3. 1. Evaluate the following. a. | - ⅝ | ⅝ b. |- 82 + 6 | | - 76 | 76 c. |3 · 10 ³| |.003|.003 2. Solve a. | x | = 1212 x = 1212 1 2 b. | m | = -8 No solution x = An absolute value cannot equal a negative number. 9-8 -

4. 3. Find the distance between the points with coordinates -4 and -193. | -193 - -4 |= | -189 |= 4. Solve | x-8 | = 25. Graph the solutions on a number line. x-8 = 25 +8 +8 x = 33 andx-8 = -25 +8 +8 x = -17        -20 -10 0 10 20 30 40 ·· -17 33 189 9-8

5. 5. Graph the expression | x-1 | on a coordinate grid. Use a graphing calculator or by hand with a table of values. For the calculator when entering the expression, it must read abs(x-1). To insert the absolute value, click 2 nd, then catalog (which is above the prgm key). Scroll down and select abs( then click enter and finish typing.