1.7B Absolute Value Inequalities & Word Problems Algebra II

Absolute Value Inequalities The inequality , where c>0, means that ax+b is between –c and c. This is equivalent to The inequality , where c>0, means that ax + b is beyond – c and c. This is equivalent to ax+b<-c or ax + b >c.

Example 1 Solve

Ex. 1 Graph the solution.

Example 2 Solve

Ex. 2 Graph the solution.

Ex 3: A manufacturer has a 0 Ex 3: A manufacturer has a 0.6oz tolerance for a bottle of salad dressing advertised as 16oz. Write and solve an absolute value inequality that describes the acceptable volumes for “16oz” bottles. Hint: If you want within the range, use If you want out of the range, use > What does this mean? If you buy a bottle of 16oz dressing, you might get one that actually has 15.4 to 16.6oz instead.

Ex 4: A city ordinance states that pools must be enclosed by a fence that is from 3 to 6 ft high. Write an absolute value inequality describing fences that don’t meet this ordinance. How do you find the tolerance? tolerance=(high end)-(avg. of low & high ends)

w-9.6>0.36 or w-9.6<-0.36 w>9.96 or w<9.24 Ex 5: A manufacturer has a tolerance of 0.36 lb for a bag of potting soil advertised as 9.6 lb. Write and solve an absolute value inequality that describes unacceptable weights for “9.6 lb” bags. w-9.6>0.36 or w-9.6<-0.36 w>9.96 or w<9.24

Assignment