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Absolute Value

Absolute Value Equations and Inequalities

|x| = 21 Recall that if |x| = a and a is positive, then x = a or x= -a. so |x| = 21 is equal to x = 21 or x = -21. Solution set is {21,-21}.
|2x-9| = 13 Since 13 is positive |2x-9| = 13, is equal to 2x-9 = 13 or 2x-9 = -13 2x = 22 or 2x = -4 x = 11 or x = -2 Solution set is {-2,11}
|5x| = 0 if a is 0 then x is 0. meaning |5x| = 0, is equal to 5x = 0. So 5x = 0 divide both sides by 5 x = 0 solution set is {0}
write an absolute value equation representing all numbers x whose distance from 0 is 15 units. The absolute value of a number x is equal to 15. solution is |x| = 15
solve |x+12| = |x-5| x+12 = x-5 12 = 5 no solution or x+12 = -(x-5) x+12 = -x+5 2x+12 = 5 2x = -7 x = -7/2 Solution set is {-7/2}
|7x+7|>0 The solution is all real numbers except the numbers that make x+7 equal to 0. First find the number that would make it 0. 7x+7 = 0 x = -1 So the solution is all real numbers except -1. solution set is (-∞, -1)U(-1,∞)
|x+5| = -30 The absolute value expression is set to equal a negative number, so the solution is: NO solution.
|2x+5|+6<25 First isolate the absolute value. subtract 6 from both sides. 2x+5<19, since 19 is positive set up as -a<x<a. -19<2x+5<19,now solve -24<2x<14 -12<x<7 solution is (-12,7)
Created by: s0498920