Aim: How do we solve absolute value inequality? Do Now: 1. Solve for x: 2. Solve for x: 3. Solve for x: x > 5 x < -1

There are always two situations (positive and negative) for the expression in the absolute symbol In order to satisfy,the value in the absolute value symbol must be more than 3. either x – 2 is positive or x – 2 is negative If x – 2 is positive then we simply use the original expression x – 2, if x – 2 is negative then we need to negate Case I. Case II. Case II can be done in a shorter way:

The procedure to solve absolute value inequalities 1. Set the expression in the absolute symbol on one side of inequality and the rest on the side 2. Take the original expression in the absolute value symbol and solve for the variable 3. Take the original expression in the absolute value symbol but change the inequality symbol to the opposite and sign of the other side of inequality, then solve for the variable

Remember: <, imply “and”, the graph is in between >, imply “or”, the graph is goes two directions

| 2x + 1| > 7 2x + 1 > 7 or –(2x + 1) >7 2x + 1 >7 or 2x + 1 <-7 x > 3 or x < -4 This is an ‘or’ statement. because of > Solve the 1 st inequality just like regular inequality Rewrite the 2nd inequality, reverse the inequality sign and negate the right side value, then solve it regularly. Finally, graph the solution 3 -4

Solve and graph: -8 10

Solve and graph 1. 2.