Solving Absolute Value Equations & Inequalities

Absolute Value (of x) Symbol lxl The distance x is from 0 on the number line. Always positive Ex: l-3l=3 -4 -3 -2 -1 0 1 2

Ex: |x| = 5 What are the possible values of x?

Solve the following |4-8| |6-4| |10+2| 2|6-8| -4|-4+1|

To solve an absolute value equation: |ax+b | = c, where c>0 To solve, set up 2 new equations, then solve each equation. ax+b = c or ax+b = -c ** make sure the absolute value is by itself before you split to solve.

Ex: Solve |6x-3| = 15

Ex: Solve |2x + 7| -3 = 8

Abs Value Inequalities Absolute value inequalities can be represented by a conjunctions and disjunctions Three different ways |x|=a X=-a or x=a

AND with LESS THAN |x|<a AND statement X>-a AND x<a -a<x<a

OR with GREATER THAN |x|>a X<-a OR x>a

Solving abs value inequalities Isolate the absolute value Rewrite as a compound inequality AND for less than, less than or equal to OR for greater than, greater than or equal to These abs value inequalities only have one variable (x) so they get graphed on a number line

Solve |2x+1|>5

Solve |4x|+16>8

Solve  

Ex: Solve & graph.

Solve & graph.

Solving Absolute Value Inequalities |ax+b| < c, where c>0 Becomes an “and” problem Changes to: –c<ax+b<c |ax+b| > c, where c>0 Becomes an “or” problem Changes to: ax+b>c or ax+b<-c