Absolute ValueThe distance bewteen 0 and a number on a number line is the absolute value of that number.
The symbol " | | " is used to represent absolute value . Absolute Value Equations EX 1: 4|x+2|= 24 4/4|x+2|= 24/4 |x+2|= 6 Case 1 : x+2= -6 -2 -2 x= -8 Case 2: x+2= 6 -2 -2 x= 4 EX 2: |x + 5| = 4 Case 1: x + 5 = 4 -5 -5 x = -1 Case 2: x + 5 = -4 -5 -5 x = -9 Absolute Value Inequalities EX 1: |x| +3 <12 -3 -3 |x| < 9 x>-9 AND x<9 EX 2: |2x − 1| < 5 -5 < 2x - 1 < 5 +1 +1 -4/2 < 2x/2 < 6/2 -2 < x < 3 |
Step by Step Explanation* The absolute value of +5 is 5: |5+|= +5
The absolute value of -5 is 5: |-5|= +5 * Since |x+2| is multiplied by 4, divide both sides by 4 to undo the multiplication. Rewrite the equation as two cases. Since 2 is added to x, subtract 2 from both sides. The solution set is {-8, 4} * The first thing you do is rewrite the problem as two separate cases with having a negative four and the other positive Once that's done you subtract both sides by 5 on both cases. Your solutions should be -1 and -9 {-1 ,-9} * Since 3 is added to |x|, subtract 3 from both sides to undo the addition. Write it out as a compound inequality. The solution set is {x: -9<x<9} * In this one you first want to rewrite the problem as -5 < 2x < 5 After you do that you then subtract one from both sides. After that you divide all parts by 2 and get a solution of {-2 < x <3} |