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Unformatted text preview: Math 1075 - Friday, 08.26.16 - [5.3, 5.4] - Absolute value equations and inequalities (2) Definition: Ix = x if x 20.- x if x 0. Also, I may be thought of as the DISTANCE from "X to zero. 14 distance from 4 to zero 4 - 4 = distance from - 4 to zero: 4 1x + 7 has 2 solutions, 7 and - 7.BUT the equation x -2 has no solution, because I can never be negative. 17 REAL, REAL IMPORTANT FIRST STEP: Isolate the absolute value IxI=3 X-3 -3 1x - 7:3 +77 14:10 21xl-7:3 +7+7 240 IxI=5 7:5,- Ixl. 5:3 - x 2 NU X19,-10 The solutions to If(x) = d will be the solution to f(x)=d, and also the solution to f(x)..d Con the graphing calculator help to solve these? 3 x +61-10 = 5 2x - 5-10=7 HICHO 12x-5-17 2x-5=17 34x+61-15 1x+61-5 xt >>X-1 28 22 2x-5:-17 X -6THEY. WHAT DO WE HAVE TO DO FIRST] 17.2-W-I = 3.8 IDIO 4 x 17.2-W -4.8 -3)*x+2)3-5 2 15 x+2)-2 7.2-W :4. -7.2 7.2 -W: -2.4 W-2. 4X+ **=0.5 (x=0 7.2-W: -4. -7.2 7.2 -W -12 W:12 5|3x 2-4 =16 5|3x-21-20 13x-2134 3x-2=4 OR 3X-23-4 3x3-2 3836x = ly means either xiyor x y x1 = x - 31 * EX-3 13y + 5 = 12y. 71 3Y+;' = 24+7 -27 -27 Yt5:7 Y+ :-27-2 27 2Y 15-3 x+13-(x-3) x+3x+3 2x+1.3 5.4. Solving absolute value linear inequalities (STILL IMPORTANT: Isolate the absolute value FIRSTU x = 3 means 1x 3 means x 3 means Impact Lent a ry Strategy for f(x)= d solve f(x) = d OR f(x) = -d E t For If(x) sd solve - d s f(x) s d For f(x) 2 d solve f(x) 20 OR f(x) sud Solvex - 2110 and write the solution in interval form. Analyze graphically, too, if time permits E -103 X-2310 +2 +2 +2 [-8,12]